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

On the minimum and maximum selective graph coloring problems in some graph classes

Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selective coloring problem in some specific graph classes motivated by some models described in Demange et al. (2015). Second, we introduce a new problem that corresponds to the worst situation in the minimum selective coloring; the maximum selective coloring problem aims to select one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is maximum. We motivat

Channel assignments using constrained greedy algorithm, T-coloring and simulated annealing in mesh and cellular networks

Channel assignment is an important step in communication networks. The objectives of minimizing networks interference and the channels used are the problems in the channel assignments of the networks. In real environments, some difference will be expected in the performance of the networks when the channel allocation algorithms under more accurate interference models are deployed. In this research, the wireless mesh networks represent dynamic networks while static networks are represented by the cellular networks. In the wireless mesh networks, communication between a pair of nodes happens when both nodes are assigned with channels. The cellular networks are the radio network distributed over land areas called cells, each served by at least one fixed-location transceiver. Channel assignments in the networks is an application of the vertex coloring in graph theory. Previously, the Greedy Algorithm was used for link scheduling but only the adjacent channel constraint was considered. Here, an algorithm called Improved Greedy Algorithm was proposed to solve the channel assignments by considering the adjacent channel and co-channel constraints which is an improvement to the algorithm. Besides, Simulated Annealing and T-coloring problem are combined to minimize the channels used. The algorithms are applied for single and multiple channels communications in the wireless mesh networks and cellular networks to show the different results of the channel assignments. Further improvement is made on the multiple channels case where the Improved Greedy Algorithm is applied by considering the cosite constraint in addition to the co-channel and adjacent channel constraints. The Improved Greedy Algorithm has been tested in a series of simulations. Results for the simulations prove that the Improved Greedy Algorithm perform significantly well for the channel assignment problem

Methods and problems of wavelength-routing in all-optical networks

We give a survey of recent theoretical results obtained for wavelength-routing in all-optical networks. The survey is based on the previous survey in [Beauquier, B., Bermond, J-C., Gargano, L., Hell, P., Perennes, S., Vaccaro, U.: Graph problems arising from wavelength-routing in all-optical networks. In: Proc. of the 2nd Workshop on Optics and Computer Science, part of IPPS'97, 1997]. We focus our survey on the current research directions and on the used methods. We also state several open problems connected with this line of research, and give an overview of several related research directions

Graph Problems arising from Wavelength-routing in All-optical Networks

International audienceThis paper surveys the theoretical results obtained for wavelength{routing all{optical networks, presents some new results and proposes several open problems. In all{optical networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on di erent wavelengths. The information, once transmitted as light, reaches its destination without being converted to electronic form inbetween, thus reaching high communication speed. We consider both networks with arbitrary topologies and particular networks of practical interest

Scheduling algorithms for throughput maximization in data networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 215-226).This thesis considers the performance implications of throughput optimal scheduling in physically and computationally constrained data networks. We study optical networks, packet switches, and wireless networks, each of which has an assortment of features and constraints that challenge the design decisions of network architects. In this work, each of these network settings are subsumed under a canonical model and scheduling framework. Tools of queueing analysis are used to evaluate network throughput properties, and demonstrate throughput optimality of scheduling and routing algorithms under stochastic traffic. Techniques of graph theory are used to study network topologies having desirable throughput properties. Combinatorial algorithms are proposed for efficient resource allocation. In the optical network setting, the key enabling technology is wavelength division multiplexing (WDM), which allows each optical fiber link to simultaneously carry a large number of independent data streams at high rate. To take advantage of this high data processing potential, engineers and physicists have developed numerous technologies, including wavelength converters, optical switches, and tunable transceivers.(cont.) While the functionality provided by these devices is of great importance in capitalizing upon the WDM resources, a major challenge exists in determining how to configure these devices to operate efficiently under time-varying data traffic. In the WDM setting, we make two main contributions. First, we develop throughput optimal joint WDM reconfiguration and electronic-layer routing algorithms, based on maxweight scheduling. To mitigate the service disruption associated with WDM reconfiguration, our algorithms make decisions at frame intervals. Second, we develop analytic tools to quantify the maximum throughput achievable in general network settings. Our approach is to characterize several geometric features of the maximum region of arrival rates that can be supported in the network. In the packet switch setting, we observe through numerical simulation the attractive throughput properties of a simple maximal weight scheduler. Subsequently, we consider small switches, and analytically demonstrate the attractive throughput properties achievable using maximal weight scheduling. We demonstrate that such throughput properties may not be sustained in larger switches.(cont.) In the wireless network setting, mesh networking is a promising technology for achieving connectivity in local and metropolitan area networks. Wireless access points and base stations adhering to the IEEE 802.11 wireless networking standard can be bought off the shelf at little cost, and can be configured to access the Internet in minutes. With ubiquitous low-cost Internet access perceived to be of tremendous societal value, such technology is naturally garnering strong interest. Enabling such wireless technology is thus of great importance. An important challenge in enabling mesh networks, and many other wireless network applications, results from the fact that wireless transmission is achieved by broadcasting signals through the air, which has the potential for interfering with other parts of the network. Furthermore, the scarcity of wireless transmission resources implies that link activation and packet routing should be effected using simple distributed algorithms. We make three main contributions in the wireless setting. First, we determine graph classes under which simple, distributed, maximal weight schedulers achieve throughput optimality.(cont.) Second, we use this acquired knowledge of graph classes to develop combinatorial algorithms, based on matroids, for allocating channels to wireless links, such that each channel can achieve maximum throughput using simple distributed schedulers. Third, we determine new conditions under which distributed algorithms for joint link activation and routing achieve throughput optimality.by Andrew Brzezinski.Ph.D

Parallel Desynchronized Block Matching: A Feasible Scheduling Algorithm for the Input-Buffered Wavelength-Routed Switch

The input-buffered wavelength-routed (IBWR) switch is a promising switching architecture for slotted optical packet switching (OPS) networks. The benefits of the IBWR fabric are a better scalability and lower hardware cost, when compared to output buffered OPS proposals. A previous work characterized the scheduling problem of this architecture as a type of matching problem in bipartite graphs. This characterization establishes an interesting relation between the IBWR scheduling and the scheduling of electronic virtual output queuing switches. In this paper, this relation is further explored, for the design of feasible IBWR scheduling algorithms, in terms of hardware implementation and execution time. As a result, the parallel desynchronized block matching (PDBM) algorithm is proposed. The evaluation results presented reveal that IBWR switch performance using the PDBM algorithm is close to the performance bound given by OPS output buffered architectures. The performance gap is especially small for dense wavelength division multiplexing (DWDM) architectures.This research has been funded by the Spanish MCyT grant TEC2004-05622-C04-02/TCM (ARPaq). Authors would like to thank also the COST 291 action and the e-Photon/ONe+ European Network of Excellence