Second International Conference on Network Analysis 2012

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24 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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Second International Conference on

Network Analysis 2012




May 7
th


May 9th, 2012





Center for Applied optimization (CAO),

University of Florida, USA



Laboratory of Algorithms and Technologies for Networks Analysis

(LATNA), Higher School of
Economics, Russia












Second

International
Conference in Network Analysis

2.


2


Mon
day,
May

7
th

Room
313

HSE,
25/12

Bolshaya

Pecherskaya
Str.


15
:
00
-
15
:
3
0
Panos M. Pardalos

Second International Conference on Network Analysis 2012


15
:
3
0
-
1
6
:
2
0
Christodoulos A. Floudas

Towards Large Scale Deterministic
Global Optimization


1
6
:
2
0
-
1
6
:
40

Coff
ee Break


1
6
:
40
-
1
8
:
10

Session 1

Ludmila Egorova

Behavioral model of stock exchange

Dmitry Malyshev

On expanding operators for the independent set problem

Dmitry Mokeev

Structural and complexial properties of P
3
-
k
ö
nig
graphs

Victor Zamaraev

A heuristics for the weighted independent set problem



Second

International
Conference in Network Analysis

2.


3


Tues
day,
May

8
th

Room
313

HSE, 25/12 Bolshaya Pecherskaya Str.


10
:
0
0
-
1
0
:
5
0
Boris Mirkin

Representing Activities by Taxonomy Concepts: Clustering and Lifting


1
0
:
5
0
-
1
1
:
1
0 Coff
ee

Break


1
1
:
1
0
-
1
2
:
3
0

Session 1

Pando G. Georgiev

Innovative tools for analyzing state transitions and evolution of complex dynamic networks

Alexey Yashunsky

Using Online Social Networks for Social Geography Studies

Alexander Rubchinsky

A New Algorithm of
Network Decomposition and its Application for Stock Market Analysis


1
2
:
30
-
1
4
:
0
0 Lunch Break


14
:
0
0
-
1
4
:
5
0
Ding
-
Zhu Du

Min
-
Weight Connected Sensor Cover and Max
-
Lifetime Target Coverage


1
4
:
5
0
-
15
:
5
0 Session 2

Anton Kocheturov

Market Graph Analysis by Means
of the P
-
Median Problem

Mikhail Batsyn

Applying Tolerances to the Asymmetric Capacitated Vehicle Routing Problem

Evgeny Maslov

Complex approach to solving the maximum clique problem


15:50
-
16:10 Coff
ee Break




Second

International
Conference in Network Analysis

2.


4


1
6
:
10
-
1
7
:
3
0 Session 3

Grigory Bautin

Markov
chains in modeling of the Russian financial market

Dmitry Gorbunov

Simulation of Pedestrian Crowds with Anticipation using Cellular Automata Approach

Pankaj Kumar

Behavioural Dynamics in Stock Market

Lazarev Evgeny Alexandrovich

Bi
-
criteria model and algor
ithms of solving data transmission network optimization problem





Second

International
Conference in Network Analysis

2.


5


Wednes
day,
May

9
th

Room
313

HSE, 25/12 Bolshaya Pecherskaya Str.


9
:
3
0
-
1
0
:
2
0
Mauricio G. C. Resende

Randomized Algorithms for the Handover Minimization Problem in Wireless
Network Design


10:20
-
10:40 Coff
ee Break


1
0
:
40
-
1
2
:
20

Session 1

D.V. Kasatkin

Synaptic cellular automaton

for description the sequentia
l dynamics of excitatory neural
networks

Pavel Sukhov

Heuristic Algorithm for the Single Machine Scheduling Problem

Ilya Bychkov

“Patterns” for solving the Cell Formation Problem

Peter Koldanov

Statistical Properties of the Market Graph


1
2
:
30
-
1
4
:
0
0 Lunch Break




Second

International
Conference in Network Analysis

2.


6


Towards Large Scale Deterministic Global Optimization


Christodoulos A. Floudas

Department of Chemical and Biological
Engineering

Princeton University
,
USA

floudas@princeton.edu


In this seminar, we will provide an overview of the research progress in deterministic global
optimization. The focus will be on important contributions during the last five years, and will
provide a perspective for future research opportunities. The overview will cover the areas of (a)
twice continuously differentiable constrained nonlinear optimization, and (b) mixed
-
integer
nonlinear optimization models. Subsequently, we will present our r
ecent fundamental advances
in (i) convex envelope results for multi
-
linear functions, and edge concave functions, (ii) a
piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii)
piecewise linear relaxations of biline
ar functions, (iv) large scale extended pooling problems,
and (v) large scale generalized pooling problems. Computational studies on medium and large
scale global optimization applications will illustrate the potential of these advances.




Second

International
Conference in Network Analysis

2.


7


Behavioral mode
l of stock exchange


Fuad Aleskerov
,

Lyudmila Egorova

National Research University Higher School of Economics
, Moscow, Russia

alesk@hse.ru, legorova@hse.ru


Due to the global financial crisis and its consequences stock exchange nowadays is an essential
element of market infrastructure, a sensitive "barometer" to the slightest changes in the economy.
For this reason the importance of the study of the stock exch
ange processes and the construction
of adequate models of the exchange game has been increased. Behavioral finance is a new
direction in financial economics, which explains the trading process based on investor
psychology and the impact of their behavior o
n the market. Recently Taleb N.N. suggested to
analyze the crises (called Black Swans) as the events with three main properties. A Black Swan
is a very rare event, it carries an extreme impact, and the occurrence of this event cannot be
predicted in advanc
e (and only after the Black Swan happened we can come up with its
explanation). Thus, the Black Swan is a metaphor for the crisis itself. Therefore everyone has to
expect these Black Swans and be ready for their occurrence. However, should all investors
f
ollow such a strategy? And should we expect a rare and unpredictable event, even with a big
impact, rather than deal with “the bird in the hand”?

To answer this question we construct a mathematical model of the stock exchange, in which the
processes are mo
deled as a reaction to the signals about the state of the economy. There are two
Poisson flows of signals/events of two types, one of which is 'regular' event that corresponds to a
stable economy and the second one is the 'crisis' event signaling about the

crisis. The intensity of
the first flow is much greater than the intensity of the crisis events (Black Swans rarity
condition). The player does not know in advance about the type of the incoming signal and have
to recognize it (the condition of unpredicta
bility). Player’s wealth depends on how well she
identifies the signals on the stock exchange, because gain/loss from the crisis event is much
greater than the gain/loss in case of the ordinary, frequent events (condition of great influence).

We showed tha
t the average player's gain will be positive if she can correctly recognize the
ordinary events in slightly more than in the half of the cases. In other words, players do not need
to play more sophisticated games, trying to identify crises events in advanc
e. This conclusion
resembles the logic of precautionary behavior, that prescripts to play the game with almost
reliable small wins. We believe that this very phenomenon lies in the basis of unwillingness of
people to expect crises permanently and to try re
cognizing them. The proposed model was tested
on stock exchange indices (S&P 500, Dow Jones, САС 40, DAX, Nikkei 225, Hang Seng, on
time interval 1999
-
2009) and on data of different shares (Microsoft, General Electric, Morgan
Chase, Proctor&Gamble, Johnson
&Johnson, Apple, AT&T, IBM, Bank of America).

Acknowledgement. We are grateful for partial financial support of the HSE International
Laboratory of Decision Choice and Analysis (DeCAn Lab) and NRU HSE Science Foundation
(grant № 10
-
04
-
0030). Lyudmila Ego
rova expresses sincere gratitude to the HSE Laboratory of
Algorithms and Technologies for Networks Analysis (LATNA
) for partial financial support
.



Second

International
Conference in Network Analysis

2.


8


On expanding operators for the independent set problem


Malyshev Dmitry Sergeevich

National Research
University Higher School of Economics,

National Research University Lobachevky State University of Nizhniy Novgorod
, Russia

dmalishev@hse.ru


All considered graphs are
simple
, i.e. undirected unlabeled graph without loops and
multiple edges. A
class of
graphs

is a set of simple graphs. A class of graphs is called
hereditary

if it is closed under deletions of vertices. It is known that a hereditary (and only hereditary class)

can be defined by a set of its
forbidden induced subgraph
s

, i.e. graphs that don't belong to
. It is denoted by
.

Let

be an NP
-
complete graph problem. A hereditary graph class

is called
-
easy

if

is polynomial
-
time solvable for graphs in
. All known to the author proofs of papers on
expansions of cases with polynomial
-
time solvability substantially use a specific character of the
old, narrower case. At the same time, it would be desirable to have «universal» such kind
generalizations. For
the family of hereditary graph classes it is offered to consider
transformations

(one
-

or many
-
variable function with arguments in a part of
),
such that

and from
-
e
asiness of

follows that

is also
-
easy. We will refer such kind transformations to
-
expanding operators
.

The case, when

is the independent set problem and
, will be only
considered further. The interest in hereditary subclasses of

is conditioned by
several causes. Firstly, if
, then the independent set prob
lem is polynomial
-
time
solvable in

if and only if

is a forest. Moreover, the case

is unique among
all connected graphs with five vertices with open computational status of the problem
for
. There are many papers in which one or more forbidden induced subgraphs are added
to

and the effective solvability of the problem for obtained graphs class is proved.
Secondly, for any graph

with at most five vertices,

and
, the problem admits a
polynomial
-
time algorithm for graphs in
. Unfortunately, its complexity is
unknown for the class
.

Two concrete expanding operators for the independent set problem will be specified
further. The
product


of

and

is the graph
. It is easy to see that the mapping

is an expanding operator for the problem. Two more such operators are
described below.


Theorem.
The mapping

is an expanding operator for the
independent set problem
.
For any natural


the mapping

is an expanding operator for the independent set
problem
.


The author is partially supported by

LATNA

Laboratory, NRU HSE, RF government
grant, ag.

11.G34.31.0057, by Russian Foundation for Basic Research, grants
11
-
01
-
00107
-
а

и

12
-
01
-
00749
-
а
, and by Federal Target Program «Academic and educational specialists of
innovative Russia», state contract
16.740.11.0310

Second

International
Conference in Network Analysis

2.


9


Structural and complexial properties of P
3
-
könig graphs


D
. B.

Mokeev

National Research University Lobac
hevky State University of Nizhniy Novgorod
, Russia

mokeevDB@mail.ru


Hereditary class of graphs in which maximum number of non
-
intersecting P
3
-
subgraphs is equal
with minimum number of vertexes contains in every such subgraphs

and polynomial recognition
algorit
hm for this class are described
.



Second

International
Conference in Network Analysis

2.


10


A heuristics for the weighted independent set problem


B.I. Goldengorin
1
, D.S. Malyshev
1,2
, P.M. Pardalos
1,3
, V.A. Zamaraev
1,2

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics,
Nizhniy Novgorod
, Russia

2
National Research University Lobachevky State University of Nizhniy Novgorod
, Russia

3
Center for Applied Opti
mization
,
University of Florida
,
Gainesville,
USA

b.goldengorin@rug.nl, dmalishev@hse.ru,
p.m.pardalos@gmail.com
,

vzamaraev@hse.ru


In this paper we design a new heuristic tolerance
-
based algorithm for solving the Weighted
Independent Set problem (the WIS,

for short). Our algorithm is based on the polynomially
solvable special case of the WIS, which is defined on trees (the WIST, for short). We show that
an optimal solution and all tolerances with respect to this solution of the WIST might be
simultaneously

found by the adjusted Chen et al. dynamic programming algorithm in O(n) time.
Based on this procedure we offer a heuristic algorithm for the WIS, which takes O(mnlog(m))
time. We also present several computational experiments for its approximation ratio,
they
showed good enough results for some models of sparse graphs.

The authors is partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag.
11.G34.31.0057
. This study comprises research findings from the ‘Calculus of tolerances in
combinatorial optimization problems: theory and algorithms’ Project carried out within The
Higher School of Economics’ 2012 Academic Fund Program.



Second

International
Conference in Network Analysis

2.


11


Representing Activities by Ta
xonomy Concepts: Clustering and Lifting


Boris Mirkin

National Research University Higher School of Economics, Moscow RF

Birkbeck University of London, London UK

bmirkin@hse.ru


Given a taxonomy

of a domain, the activities of an organization in the domain can be represented
by crisp or fuzzy clusters of the corresponding taxonomy leaf concepts

(thematic clusters). To
represent a thematic cluster in the taxonomy, a parsimonious

lifting method is
developed. The
method maps the cluster’s topics to higher ranks of the

taxonomy tree. The lifting criterion
involves a penalty fun
ction summing penalties for the

"head" subjects together with penalties for
emerging gaps and offshoots. The developments are

illustrated by using synthetic and real
-
world
data.



Second

International
Conference in Network Analysis

2.


12


Innovative tools for analyzing state trans
itions and evolution of complex
dynamic networks


Pando G. Georgiev and Panos M. Pardalos


Center for Applied Optimization

University of Florida
,
Gainesville,
U
SA

pandogeorgiev@ufl.edu
,
p.m.pardalos@gmail.com


The problem of detection and prediction of changes (state transitions), dependences

and
causalities in the evolution of complex networks is of tremendous significance.

Several
important practical networks
desperately need tool
s for prediction, for instance:
in biological
networks
-

epileptic brain networks for prediction of epileptic seizures;

in

power system
networks
-

electric grid, for prediction of blackouts; in social networks
-

for prediction of
malic
ious behaviors of some social groups, etc.

We present several innovative tools applicable to this problem:

1) Reproducing Kernel Banach Spaces.

We extend the idea of Reproducing Kernel Hilbert Spaces to Banach spaces (and beyond),

developing a theory
without the requirement of existence of semi
-
inner product

(which

requirement is already explored in another construction of RKBS). We apply

our construction to
the basic learning algorithms, including support vector machines,

kernel regression, kernel
pri
ncipal component analysis. We demonstrate the better

adaptive features of such spaces to new
dimensionality reduction techniques and to detection of state transitions in some complex
networks, as epileptic brain. We introduce

a qualitative new concept ”mul
tiple reproducing
kernels”, which encompasses not only

bivariate, but also multivariate connections between data
variables, arranging them in

a kernel tensor
-

a generalization of the kernel matrix.

2) Tensor decompositions.

Multi
-
way structures of the dat
a has been widely ignored in many fields of research,

especially
in dynamical complex networks. The functional MRI is another typical

example, where the data
is inheritably tensorial. Collapsing some of the modes to form

of a matrix or vector leads to loss

of information. Many tensor representations admit

uniqueness of the decomposition without
additional constraints such as orthogonality

(as in Singular value decomposition, or PCA) or
independence (as in Independent

Component Analysis). We review some tens
or decomposition
methods and introduce

new ones, involving sparsity, suitable for complex sparse networks.

3) Adaptive multi
-
class learning problems.

We generalize the main task of statistical learning theory to multiclass learning

problems,
allowing
several classes approximating functions to choose adaptively from

several classes of
data (possibly heterogeneous).

4) Nonlinear skeletons of data sets and skeleton classifiers.

A particular case of multiclass learning problems is the problem of subspace c
lustering, which
we extend to RKBS defining in such a way the concept of nonlinear

skeletons and its derivative,
Skeleton Classifier.

5) Trajectory reconstruction.

Square roots, or more generally, iterative roots of operators are of interest in dynamical s
ystems,
chaos and complexity theory and also in the modeling of certain

industrial and financial
Second

International
Conference in Network Analysis

2.


13


processes. An operator f acting from a set X to X, satisfying

the functional equation f(f(x)) =
F(x) (for every x from X) is called ”square root”

of the given
operator F acting from X to X. The
problem of computing square roots

of operators (if exists) remains a hard task. While the theory
of functional equations

provides some insight for the iterative roots of real and complex valued
functions, iterative roots
of mappings in high dimensional spaces are almost not studied and
there

are little contributions to numerical algorithms for their computation. We prove existence
of iterative roots of a certain class of monotone mappings in Hilbert spaces,

generalizing th
e
scalar case result for strictly monotone functions. We demonstrate

how methods based on neural
networks and statistical learning theory can find square

roots of trajectories of certain dynamical
systems.



Second

International
Conference in Network Analysis

2.


14


Using Online Social Networks for Social Geograph
y Studies


Alexey Yashun
sky
1

and Nadezda Zamiatina
2

1
Keldysh Institute of Applied Mathematics
, Russia

2
Geography
D
epartment,
Moscow State University
, Russia

yashunsky@keldysh.ru,
nadezam@mail.ru


Research in social and economic geography more often than not relies on various statistics as
raw data. Hence, the lack of trustworthy and detailed statistical materials may become a
hinderance. Whereas developed countries (e.g. USA, EU countries) have vas
t statistic databases
open to the public, the emerging economies and developing countries to this day still have very
limited statistical information available.

This statistical vacuum forces researchers to look for other sources of information. These can
be
found, for instance, within online social networking services. Although this information is hardly
representative of the entire population and never absolutely trustworthy, it can still be used to
study certain social groups.

These research techniques m
ay be of interest even for developed countries for studying
phenomena that are not reflected by official statistics.

We have recently carried out some basic research on "knowledge spillover" in modern Russia
using public data from the vk.com social network
. The studied cases revealed some interesting
spacial patterns in the origin and later employment locations of several Russian Universities'
students. Further and deeper analysis may allow identification of the so
-
called bonding and
bridging connections fo
r Universities and trace their spacial components so as to evaluate their
influence on creative and labor force migrations in modern Russia.

The challenges for network analysis in this area are both technical and theoretical. On the one
hand, processing so
cial network data with geographical goals requires the development of
specific tools, on the other hand, formal network
-
level criteria could help the identification of
certain geography
-
specific phenomena.



Second

International
Conference in Network Analysis

2.


15


A New Algorithm of Network Decompositio
n and its Application for Stock
Market Analysis


Boris Goldengorin
1
, Panos Pardalos
1
,2
,
A
lexander

Rubchinsky
1

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

b.goldengorin@rug.nl,

p.m.pardalos@gmail.com
,

arubchinsky@yahoo.com


The network decomposition problem is one of the well
-
known «classical» problems of network
analysis. Informal character and great diversity of applications have led to many different formal
statements of the problem. The essence of the suggested approach c
onsists in a new combination
of two known ideas: finding a cut by
the
so called frequency method and checking statistical
stability of obtained divisions. In both directions new modifications
a
re suggested.

The algorithm is constructed as a multistage pro
cedure. A result of every stage is a family of
decompositions that firstly is gradually expanded and after gradually contracted so that the
output of the entire procedure

consists of one decomposition.

The essential features of the suggested approach are f
ormulated as follows.

1. The number of parts is determined by the algorithm itself. Particularly, the algorithm can
establish the absence of reasonable divisions (at least, in the framework of the suggested
method).

2. The output can produce not only decom
positions but single parts and their families as well.

3. There are only few (for such a universal scheme) meaningful parameters.

The approach
i
s
applied

to analysis of data from stock markets of USA, Sweden and Russia. The
only input data consists of all

the pairwise correlations between prices of stocks. The network is
constructed as follows. Its vertices correspond to stocks; any vertex is connected to 4 closest
(with the maximal correlation coefficients) vertices. Stable clusters were revealed in USA a
nd
Russia
n

stocks. They correspond to firms engaged in the same or close kinds of activity (for
instance, in USA in gold mining and investment, in Russia in electricity production). In Sweden
market the algorithm

does not reveal stock clusters
.



Second

International
Conference in Network Analysis

2.


16


Min
-
Weight Connected Sensor Cover and Max
-
Lifetime Target Coverage


Ding
-
Zhu Du

University of Texas at Dallas, USA

dzdu@utdallas.edu


It was open for many years whether the target coverage problem has a polynomial
-
time constant
-
approximation or not. In
this talk, we introduce a solution, 3.65
-
approximation, which is a new
result in our research group in UTD (University of Texas at Dallas).

The target coverage problem can be stated as follows:

Suppose each sensor has unit lifetime and a unit disk as its c
overage area. Given a set of target
-
points and a set of sensors in the Euclidean plane, find a sensor sleep/activate schedule to
maximize the lifetime under constraint that every target
-
point is monitored by at least one sensor
during the lifetime. This co
nstant
-
approximation is established by its connection to minimum
weight connected sensor cover problem.



Second

International
Conference in Network Analysis

2.


17


Market Graph Analysis by
M
eans of the P
-
Median
P
roblem


Mikhail Batsyn
1
, Boris Goldengorin
1
,
Anton Kocheturov
1
,
Panos Pardalos
1
,2

1
Laboratory of
Algorithms and Technologies for Network Analysis
,
National Research
University Higher School of Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

mbatsyn@hse.ru, b.goldengorin@rug.nl,

antrubler@gmail.com
,
p.m.pardalos@gmail.com


In this work we apply pseudo
-
B
oolean approach to
analysis of
stock

market graphs
. We
divide

market graphs
into clusters of highly correlated stocks
by means of the

p
-
Median model and
search
for
regularity in
the
calculated results. Our final

goal

is to
provide

a new tool
for

a deep
er
understanding of the

market
structure dynamics
.



Second

International
Conference in Network Analysis

2.


18


Applying Tolerances to the Asymmetric Capacitated Vehicle Routing Problem


Mikhail Batsyn
1
, Boris Goldengorin
1
, Panos Pardalos
1
,2

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia


2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

mbatsyn@hse.ru, b.goldengorin@rug.
nl,

p.m.pardalos@gmail.com


In this talk we consider the Asymmetric Capacitated Vehicle Routing Problem (ACVRP). We
solve the ACVRP with two different versions of branch
-
and
-
bound algorithm. The first one is
the classical branch
-
and
-
bound algorithm which
uses the cost
-
based branching

rule
. The second
one is a new branch
-
and
-
bound algorithm in which we first take the branch which has the
minimal tolerance. Such a tolerance
-
based approach was suggested by Boris Goldengorin,
Gerard Sierksma and Marcel Turkens
teen (2004) and proved its efficiency for the Asymmetric
Travelling Salesman Problem (ATSP). We compare the number of search tree nodes and
computational time
s

for the
se

two algorithms on several ACVRP instances and show that
tolerance
-
based branching
rule

is more
efficient
.

We also present a new heuristic algorithm for the ACVRP which can be related to the class of
cluster
-
first route
-
second heuristics. On the first stage the vertices are divided into K clusters by
solving the Capacitated P
-
Median Problem
so that all the vertices from one cluster can be visited
by one of the K vehicles. This problem is solved exactly by means of the pseudo
-
B
oolean
p
-
median
model suggested by Boris Goldengorin

and his co
-
authors in 2009
-
2011. On the second
stage the ATSP pro
blem is solved exactly for each cluster again using a tolerance
-
based
approach. After these two stages we iteratively move vertices between the found routes while the
objective function is improved. Among all the vertices we move that vertex from one route

to
another, for which this movement is feasible and the improvement of the objective function is
maximal.



Second

International
Conference in Network Analysis

2.


19


A
Com
bined

A
pproach to
S
olving the
M
aximum
C
lique
P
roblem


Mikhail Batsyn
1
, Boris Goldengorin
1
, Evgeny Maslov
1
, Panos Pardalos
1
,2

1
Laboratory of
Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

mbatsyn@hse.ru, b.goldengorin@rug.nl,

lyriccoder@gm
ail.com
,

p.m.pardalos@gmail.com


In this talk we suggest a
combined

approach to solving
the M
ax
imum

C
lique
P
roblem

(MCP)
. It
is based on
two classical NP
-
hard combinatorial optimization problems: the
G
raph
C
oloring
P
roblem

(GCP)

and the
M
aximum
I
ndependent
S
et
P
roblem

(MISP)
. We use
heuristic

solution
s

of these problems to improve the performance of our exact algorithm. Following the MCS
algorithm (Tomita, Sutani, Higashi, Takahashi and Wakatsuki, 2010), graph coloring is used as a
branching strat
egy for finding the maximum clique. A heuristic solution of
the MISP
for the
complement graph
returns
a good lower bound for the
MCP
and improves the performance of the
algorithm. Moreover, if colors are first assigned to those vertices which are in the la
rge cliques,
then the large search sub
-
trees related to such vertices are pruned due to the small color numbers.
W
e have
also
improved the sequential graph coloring
suggested
by Tomita, Sutani, Higashi,
Takahashi and Wakatsuki (2010).

We illustrate our fin
dings by means of a computational study
for the MCP
.



Second

International
Conference in Network Analysis

2.


20


Markov chains in modeling of the Russian financial market


Grigory Bautin

and

Valery Kalyagin

Laboratory of Algorithms and Technologies for Network Analysis

National Research University Higher School
of Economics, Nizhny Novgorod, Russia

greg.bautin@gmail.com
, vkalyagin@hse.ru


We consider a Markov chains model for the problem of multiperiod portfolio optimization, and
apply it to the Russian stock market. Due to higher volatility and other peculiariti
es of the
Russian market, the known approaches produce the phenomena of non stability. We propose
enhancements to
the model in order to smooth it
.



Second

International
Conference in Network Analysis

2.


21


Simulation of Pedestrian Crowds with Anticipation using Cellular Automata
Approach


Mikhail Batsyn
1
, Boris
Goldengorin
1
,
Dmitry Gorbunov
1
,
Panos Pardalos
1
,2

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

mbatsyn@hse.ru, b.goldengorin@rug.nl,

dmigorbunov@gmail.com
,

p.m.pardalos@gmail.com


Recently,
cellular automata

have been applied to models of traffic and evacuation without mental
properties.

Goldengorin, Krushinsky and Makarenko ha
ve

sh
own that
three criteria namely the
minimization of evacuation time, maximization of instantaneous flow of pedestrians, and
maximization of mentality
-
based synchronization of a crowd are interdependent.

In this talk
we
discuss our implementation of
this model and
its potential application to study networks of
neurons
.



Second

International
Conference in Network Analysis

2.


22


Behavioural Dynamics in Stock Market


Pankaj Kumar

Perm State National Research

University, Russian Federation

kumar.x.pankaj@gmail.com


Stock market is an example of complex system,
which is characterized by a highly intricate
organization and the emergence of collective

behaviour. In this paper, we quantify this
behavioural dynamics in

the stock market by using concepts of network synchronization. We

consider networks constructed by
the correlation matrix of asset returns and study the time
evolution of the phase coherence among

stock prices. It is veri
fi
ed that during

fi
nancial crisis a

synchronous

state emerges in the system, de
fi
ning the market's direction. Furthermore, the paper
p
roposes a statistical regression model able to

i
dentify the network topological features that

mostly in
fl
uence such

an emergence. The coe
ffi
cients of the proposed model indicate that

the
average shortest path length is the measurement most related to

netwo
rk synchronization.
Therefore, during economic crisis, the stock

prices present a similar evolution, which tends to
shorten the distances

between stocks, indication a collective behavioural dynamics.



Second

International
Conference in Network Analysis

2.


23


Bi
-
criteria model and algorithms of solving data
transmission network
optimization problem


Lazarev Evgeny Alexandrovich
,
Misevich Pavel Valerievich
, Shaposhnikov Dmitry Evgenievich

Nizhny Novgorod State Technical University n.a. R.E. Alexeev, Nizhny Novgorod, Russia

elazarev.nnov@gmail.com
,
p_misevich@mail.ru
,
dm.shaposhnikov@gmail.com


A data transmission network model based on classic network
-
flow models is proposed.
Consider acyclic oriented graph
, describing existing data transmission network.
Vertices of the graph
represent multiplexers of the network. Edge

connects vertices

and
, represents the data channel and has positive capacity
. Two vertices of the
graph

and

are considered information source and sink respectively.

The set

(
) describes data channels which can be added to the network.
The capacity

and construction cost

is given for each edge
.

The amount of information which can be transmitted over the data channel per time unit
is defined by the flow function

(

describes the flow between vertices

and
).

It is necessary to modify existing network by construction some channels of the set

to
increase the maximum network flow. A possible solution


of the problem is a set of edges
. Two

optimization

criteria

are

considered:

1.

The cost of data channels construction:

2.

The maximum network flow:
,

described

by

the

graph

.

Optimization problem:

for given acyclic oriented graph

and the set of
edges
, capacity matrices
,

and construction cost matrix

find the set of Pareto
-
optimal solutions of problem
.

It is proven that cardinality of the Pareto
-
optimal solutions set can have exponential
dependence on the problem dimension (cardinality of
). Also, it is proven that the problem is
NP
-
hard (the knapsack problem is polynomially reduced to the considered problem).

Taking into account assumption that

and computational difficulty of the problem
heuristic methods are proposed to find sub
-
optimal solutions for the considered problem. The
paper presents exact algorithms based on branch and bound method, heuristic algorithms based
on genetic algorithms and

simulated annealing algorithm and results of computational
experiments.



Second

International
Conference in Network Analysis

2.


24


Randomized Algorithms for the Handover Minimization Problem in Wireless
Network Design


Mauricio G. C. Resende

Algorithms & Optimization Research Department

AT&T Labs Research

Shannon Laboratory, Florham Park, New Jersey
, USA

mgcr@research.att.com


Mobile wireless devices connect to an antenna tower to which it has a strong signal. As the
device moves it may connect to a sequence of towers. The process that takes place when a
device changes the tower to which it is connected to is called handover (or handoff). Handovers
are not done by the tower itself but rather by the radio network controller

(RNC) to which the tower is connected. Each tower has associated with it a traffic

level which
depends, for example, on where it is located. One or more towers can connect to an RNC but
each RNC can handle a maximum amount of traffic thus limiting the subsets of towers that can
connect to it. Handovers between towers connected to diffe
rent RNCs tend to fail more often
than those between towers connected to the same RNC.

Handover failure causes a dropped call which one would prefer to avoid.

Therefore minimizing the number of handovers between towers connected to different RNCs
may lead
to a more reliable level of wireless service.

Given a set of towers, each with a given amount of traffic, a set of RNCs, each with a given
capacity, and a matrix specifying the number of handovers between pairs of towers, the
HANDOVER MINIMIZATION PROBLEM
(HMP) seeks an assignment of towers to RNCs
such that the RNC capacity is not violated and the number of handovers between towers
connected to different RNCs is minimized.

We describe three randomized heuristics for solving the HMP. The first is a GRASP w
ith path
-
relinking for the generalized quadratic assignment problem. The other two are specially tailored
for the HMP. One is is a GRASP with evolutionary path
-
relinking and the other is a biased
random
-
key genetic algorithm.

We compare these heuristics
on a set of randomly generated instances as well as on real
-
world
networks from a large wireless provider.



Second

International
Conference in Network Analysis

2.


25


Synaptic cellular automaton for description the sequential dynamics of
excitatory neural networks


D.V. Kasatkin
1
, A.S. Dmitrichev
1
, V.I. Nekorkin
1
,2

1
Institute of Applied Physics of the Russian Academy of Sciences
, Nizhny Novgorod, Russia

2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics,
Nizhniy Novgorod
, Russia

kasatkin@neuron.appl.sci
-
nnov.ru
,
admitry@neuron.appl.sci
-
nnov.ru
,
vnekorkin@neuron.appl.sci
-
nnov.ru


One of the significant problems of neurodynamics is development of analytical methods for
studying of models of complex neural networks. We present an app
roach for analyzing the
dynamics of excitatory neural networks. It consists in reducing continuous dynamics of neural
networks to a discrete dynamical systems in the form of a cellular automaton (CA) on the graph
of connections. In the approach the main ro
le is played by the dynamics of synapses but not by
the specific features of neurons. In fact, the CA represents a network of synapses with a finite
number of states which alternate each other according to some fixed rules. To determine the
rules one needs

to study only the responses of an individual synapse onto actions of neighboring
(in graph of connections) synapses through corresponding neurons. As a result the numerical
integration of the whole system of ordinary differential equations (ODEs) is not n
eeded.
Moreover, since the form of the neuron responses is not important, the approach is applicable to
a broad set of networks including those consisting of neurons, which possess the neural
excitability property (neuro
ns of the class 2 excitability)
.



Second

International
Conference in Network Analysis

2.


26


H
euristic Algorithm for the Single Machine Scheduling Problem


Boris Goldengorin
1
, Panos Pardalos
1
,2
,
Pavel Sukhov
1

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod,
Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

b.goldengorin@rug.nl,

p.m.pardalos@gmail.com
,
pavelandreevith@rambler.ru


There are
three

single machine scheduling problems

with an open computational complexity
status
. One
of them, the preemptive single machine scheduling problem of minimizing the total
weighted completion time with equal processing times and arbitrary release dates, will be
discussed in this talk. We are going to describe three heuristics for th
is

scheduli
ng problem. Two
of them
are
based on it's linear assignment problem reduction, and one based on the WSRPT
(weighted shortest remaining processing time) rule.

Our computational experiments show that
the WSRPT rule based heuristic returns either an exact opt
imal or a high quality schedule.



Second

International
Conference in Network Analysis

2.


27


“Patterns” for solving the Cell Formation Problem


Mikhail Batsyn
1
,
Ilya Bychkov
1
,
Boris Goldengorin
1
, Panos Pardalos
1
,2

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher

School of Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

mbatsyn@hse.ru,
il.bychkov@gmail.com
, b.goldengorin@rug.nl,

p.m.pardalos@gmail.com


In this paper we define the notion of a

pattern” which is closely connected with the Assignment
Problem solution and show how to apply it for solving one well
-
known combinatorial
optimization problem, namely the Cell Formation Problem. Our iterative algorithm is based on
flexible adjustments of
the given collection of cells starting with an initial solution. The
algorithm terminates when all possible adjustments of shapes and sizes for each cell and the
current collection of all cells cannot be improved by means of the prespecified objective func
tion
value. Sometimes such iterations may lead to patching a pair of neighboring cells or splitting
each cell in a number of cells. Experiments with th
e number of cells
allow us to increase the
objective function values for some cell formation problem benc
hmark instances.



Second

International
Conference in Network Analysis

2.


28


Statistical Properties of the Market Graph


Valery Kalyagin
1
, Alexander Koldanov
1
, Peter Koldanov
1
,
Panos Pardalos
1
,2

1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of
Economics, Nizhny Novgorod, Russia

2
Center for Applied Optimization
,
University of Florida
,
Gainesville,
USA

vkalyagin@hse.ru, a
koldanov
@hse.ru,

pkoldanov
@hse.ru
,
p.m.pardalos@gmail.com


The paper deals with the statistical analysis of the construction method of the market graph
introduced in [Boginski, Butenko and Pardalos 2003]. The main goal of the paper is the
investigation of the optimality of the method of construction of the market

graph from the
statistical point of view. According to the classical approach by Wald the optimal statistical
procedures is the statistical procedures with the minimal conditional risk in a fixed class. In our
investigation we consider the class of unbias
ed statistical procedures. As a statistical model of
the financial market we use the classical model by Markowitz. According to this model the
returns of financial stocks have a multivariate normal distribution defined by the vector of their
means and the
covariance matrix. The market graph (true market graph) is the matrix with
entries 0 and 1, where we put 0 if the associated correlation is less then given threshold and 1
otherwise. Sample market graph is the market graph constructed from the sample corr
elations.
The main question discussed in this paper is the relation between true and sample market graphs.
The construction method of the market graph introduced in [Boginski, Butenko and Pardalos
2003] can be considered as a statistical procedure for the
construction of the true market graph
from the sample market graph. We show that this method is optimal in the class of unbiased
multiple decision statistical procedures. To prove this result we put the problem in the
framework of Lehman theory of multip
le decision statistical procedures and precise the choice of
generating hypo
thesis
.