Secluded Connectivity Problems

Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a path $P$ can be measured as the number of nodes adjacent to it, denoted by $N[P]$. A path is said to be secluded if its exposure is small. A similar measure can be applied to other connected subgraphs, such as Steiner trees connecting a given set of terminals. Such subgraphs may be relevant due to considerations of privacy, security or revenue maximization. This paper considers problems related to minimum exposure connectivity structures such as paths and Steiner trees. It is shown that on unweighted undirected $n$-node graphs, the problem of finding the minimum exposure path connecting a given pair of vertices is strongly inapproximable, i.e., hard to approximate within a factor of $O(2^{\log^{1-\epsilon}n})$ for any $\epsilon>0$ (under an appropriate complexity assumption), but is approximable with ratio $\sqrt{\Delta}+3$, where $\Delta$ is the maximum degree in the graph. One of our main results concerns the class of bounded-degree graphs, which is shown to exhibit the following interesting dichotomy. On the one hand, the minimum exposure path problem is NP-hard on node-weighted or directed bounded-degree graphs (even when the maximum degree is 4). On the other hand, we present a polynomial algorithm (based on a nontrivial dynamic program) for the problem on unweighted undirected bounded-degree graphs. Likewise, the problem is shown to be polynomial also for the class of (weighted or unweighted) bounded-treewidth graphs

Independent-Set Reconfiguration Thresholds of Hereditary Graph Classes

Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In this paper, rather than asking this question from an algorithmic perspective, we analyze the combinatorial structure behind it. We consider the problem of reconfiguring one independent set into another, using two different processes: (1) exchanging exactly k vertices in each step, or (2) removing or adding one vertex in each step while ensuring the intermediate sets contain at most k fewer vertices than the initial solution. We are interested in determining the minimum value of k for which this reconfiguration is possible, and bound these threshold values in terms of several structural graph parameters. For hereditary graph classes we identify structures that cause the reconfiguration threshold to be large

On the dynamics of the glass transition on Bethe lattices

The Glauber dynamics of disordered spin models with multi-spin interactions on sparse random graphs (Bethe lattices) is investigated. Such models undergo a dynamical glass transition upon decreasing the temperature or increasing the degree of constrainedness. Our analysis is based upon a detailed study of large scale rearrangements which control the slow dynamics of the system close to the dynamical transition. Particular attention is devoted to the neighborhood of a zero temperature tricritical point. Both the approach and several key results are conjectured to be valid in a considerably more general context.Comment: 56 pages, 38 eps figure

Resource Allocation in Communication and Social Networks

abstract: As networks are playing an increasingly prominent role in different aspects of our lives, there is a growing awareness that improving their performance is of significant importance. In order to enhance performance of networks, it is essential that scarce networking resources be allocated smartly to match the continuously changing network environment. This dissertation focuses on two different kinds of networks - communication and social, and studies resource allocation problems in these networks. The study on communication networks is further divided into different networking technologies - wired and wireless, optical and mobile, airborne and terrestrial. Since nodes in an airborne network (AN) are heterogeneous and mobile, the design of a reliable and robust AN is highly complex. The dissertation studies connectivity and fault-tolerance issues in ANs and proposes algorithms to compute the critical transmission range in fault free, faulty and delay tolerant scenarios. Just as in the case of ANs, power optimization and fault tolerance are important issues in wireless sensor networks (WSN). In a WSN, a tree structure is often used to deliver sensor data to a sink node. In a tree, failure of a node may disconnect the tree. The dissertation investigates the problem of enhancing the fault tolerance capability of data gathering trees in WSN. The advent of OFDM technology provides an opportunity for efficient resource utilization in optical networks and also introduces a set of novel problems, such as routing and spectrum allocation (RSA) problem. This dissertation proves that RSA problem is NP-complete even when the network topology is a chain, and proposes approximation algorithms. In the domain of social networks, the focus of this dissertation is study of influence propagation in presence of active adversaries. In a social network multiple vendors may attempt to influence the nodes in a competitive fashion. This dissertation investigates the scenario where the first vendor has already chosen a set of nodes and the second vendor, with the knowledge of the choice of the first, attempts to identify a smallest set of nodes so that after the influence propagation, the second vendor's market share is larger than the first.Dissertation/ThesisPh.D. Computer Science 201

Data gathering techniques on wireless sensor networks

The nearly exponential growth of the performance/price and performance/size ratios of computers has given rise to the development of inexpensive, miniaturized systems with wireless and sensing capabilities. Such wireless sensors are able to produce a wealth of information about our personal environment, in agricultural and industrial monitoring, and many other scenarios. Each sensor due to its miniature nature has severe resource constraints in terms of processing power, storage space, battery capacity and bandwidth of radio. Our goal in this research is to maximize the extraction of information out of the sensor network by efficient resource utilization

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM