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104
ConflictFree Colorings of Simple Geometric Regions with Applications to Frequency Assignment in Cellular Networks
, 2002
"... Motivated by a frequency assignment problem in cellular networks, we introduce and study a new coloring problem that we call Minimum ConflictFree Coloring (MinCFColoring). In its general form, the input of the MinCFcoloring problem is a set system (X, S), where each S 2 S is a subset of X . The ..."
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Cited by 60 (8 self)
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Motivated by a frequency assignment problem in cellular networks, we introduce and study a new coloring problem that we call Minimum ConflictFree Coloring (MinCFColoring). In its general form, the input of the MinCFcoloring problem is a set system (X, S), where each S 2 S is a subset of X . The output is a coloring of the sets in S that satisfies the following constraint: for every x 2 X there exists a color i and a unique set S 2 S, such that x 2 S and (S) = i. The goal is to minimize the number of colors used by the coloring .
Spectrum sharing with distributed interference compensation
 IN PROC. OF IEEE DYSPAN
, 2005
"... We consider a spectrum sharing problem in which each wireless transmitter can select a single channel from a set of available channels, along with the transmission power. An Asynchronous Distributed Pricing (ADP) scheme is proposed, in which users exchange “price ” signals, that indicate the negativ ..."
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Cited by 55 (0 self)
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We consider a spectrum sharing problem in which each wireless transmitter can select a single channel from a set of available channels, along with the transmission power. An Asynchronous Distributed Pricing (ADP) scheme is proposed, in which users exchange “price ” signals, that indicate the negative effect of interference at the receivers. Given this set of prices, each transmitter chooses a channel and power level to maximize its net benefit (utility minus cost). We show that a sequential version of this SingleChannel (SC)ADP algorithm converges with two users and an arbitrary number of channels, and observe via simulation that it exhibits rapid convergence with more users in the network. The pricing algorithm always outperforms the heuristic algorithm in which each user picks the best channel without exchanging interference prices. In a dense network with heavy interference, the SCADP algorithm can also perform better than the iterative waterfilling algorithm where each user transmits over multiple channels but the users do not exchange any information. The performance of the SCADP algorithm is also compared with a MultiChannel (MC)ADP algorithm in which users can transmit over multiple channels and exchange interference prices over each channel. I.
The L(h, k)Labelling Problem: A Survey and Annotated Bibliography
, 2006
"... Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at l ..."
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Cited by 29 (3 self)
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Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)labelling with minimum span. The L(h, k)labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.
Feasible Network Configurations for UMTS
, 2002
"... A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixedinteger variables and (essentially) linear constraints. These constraints reflect the limite ..."
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Cited by 22 (7 self)
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A model for the optimisation of the location and configuration of base stations in a UMTS network is described. The focus is primarily on modelling the configuration problem sufficiently accurate using mixedinteger variables and (essentially) linear constraints. These constraints reflect the limited downlink code capacity in each cell, the interference limitations for successful up and downlink transmissions, the need for sufficiently strong (cell) pilot signals, and the potential gain for mobiles from being in soft(er) handover. It is also explained how to use the model as a basis for rating network configurations.
Branch and Tree Decomposition Techniques for Discrete Optimization
, 2005
"... This chapter gives a general overview of two emerging techniques for discrete optimization that have footholds in mathematics, computer science, and operations research: branch decompositions and tree decompositions. Branch decompositions and tree decompositions along with their respective connectiv ..."
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Cited by 21 (3 self)
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This chapter gives a general overview of two emerging techniques for discrete optimization that have footholds in mathematics, computer science, and operations research: branch decompositions and tree decompositions. Branch decompositions and tree decompositions along with their respective connectivity invariants, branchwidth and treewidth, were first introduced to aid in proving the Graph Minors Theorem, a wellknown conjecture (Wagner’s conjecture) in graph theory. The algorithmic importance of branch decompositions and tree decompositions for solving NPhard problems modelled on graphs was first realized by computer scientists in relation to formulating graph problems in monadic second order logic. The dynamic programming techniques utilizing branch decompositions and tree decompositions, called branch decomposition and tree decomposition based algorithms, fall into a class of algorithms known as fixedparameter tractable algorithms and have been shown to be effective in a practical setting for NPhard problems such as minimum domination, the travelling salesman problem, general minor containment, and frequency assignment problems.
Stochastic local search algorithms for the graph set Tcolouring . . .
 APPROXIMATION ALGORITHMS AND METAHEURISTICS; COMPUTER AND INFORMATION SCIENCE SERIES
, 2005
"... The graph set Tcolouring problem (GSTCP) generalises the classical graph colouring problem; it asks for the assignment of sets of integers to the vertices of a graph such that constraints on the separation of any two numbers assigned to a single vertex or to adjacent vertices are satisfied and some ..."
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Cited by 17 (3 self)
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The graph set Tcolouring problem (GSTCP) generalises the classical graph colouring problem; it asks for the assignment of sets of integers to the vertices of a graph such that constraints on the separation of any two numbers assigned to a single vertex or to adjacent vertices are satisfied and some objective function is optimised. Among the objective functions of interest is the minimisation of the difference between the largest and the smallest integers used (the span). In this article, we present an experimental study of local search algorithms for solving general and large size instances of the GSTCP. We compare the performance of previously known as well as new algorithms covering both simple construction heuristics and elaborated stochastic local search algorithms. We investigate systematically different models and search strategies in the algorithms and determine the best choices for different types of instance. The study is an example of design of effective local search for constraint optimisation problems.
Exact solution of a class of frequency assignment problems in cellular networks and other regular grids
 in: 8th Italian Conf. Theor. Comp. Sci. (ICTCS’03), LNCS
, 2003
"... For any non negative real values h and k, an L(h, k)labeling of a graph G = (V, E) is a function L: V → IR such that L(u) − L(v)  ≥ h if (u, v) ∈ E and L(u) − L(v)  ≥ k if there exists w ∈ V such that (u, w) ∈ E and (w, v) ∈ E. The span of an L(h, k)labeling is the difference between th ..."
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Cited by 13 (6 self)
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For any non negative real values h and k, an L(h, k)labeling of a graph G = (V, E) is a function L: V → IR such that L(u) − L(v)  ≥ h if (u, v) ∈ E and L(u) − L(v)  ≥ k if there exists w ∈ V such that (u, w) ∈ E and (w, v) ∈ E. The span of an L(h, k)labeling is the difference between the largest and the smallest value of L, so it is not restrictive to assume 0 as the smallest value of L. We denote by λh,k(G) the smallest real λ such that graph G has an L(h, k)labeling of span λ. The aim of the L(h, k)problem is to satisfy the distance constraints using the minimum span. In this paper, we study L(h, k)labeling problem on regular grids of degree 3, 4, 6, and 8 solving several open problems left in the literature. Keywords: L(h,k)labeling, triangular grids, hexagonal grids, squared grids, octagonal grids. 1
Decentralized intercell interference coordination by autonomous spectral reuse decisions
 in Proc. European Wireless Conference (EW 2008
, 2008
"... Abstract—Future wireless packet switched cellular networks will require dense frequency reuse to achieve high capacity. At the same time, measures are required which limit the interference on the frequency carriers. It is assumed that central entities performing the task of interference coordination ..."
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Cited by 12 (2 self)
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Abstract—Future wireless packet switched cellular networks will require dense frequency reuse to achieve high capacity. At the same time, measures are required which limit the interference on the frequency carriers. It is assumed that central entities performing the task of interference coordination with global knowledge should be avoided. Rather, distributed algorithms are sought for. To this end, we propose decentralized resource allocation algorithms that enable base stations to select a pool of favorable resources with low interference based on local knowledge only. The actual userlevel resource allocation from that pool will then be performed by fast schedulers operating on the preselected resources within each cell. We analyze and evaluate the proposed resource selection algorithms by introducing a simplified wireless network model and applying methods from game theory. Proving the existence of Nash equilibria shows that stable resource allocations can be reached by selfish agents. In addition to that, we perform simulations to determine the speed of convergence and the resulting equilibrium interference levels. By comparing these to an optimal global solution, which is derived by solving an integer linear program, we are able to quantify the efficiency loss of the distributed game approach. It turns out that even though the distributed game results are suboptimal, the low degree of system complexity and the inherent adaptability make the decentralized approach promising especially for dynamic scenarios. I.
Graph Labellings with Variable Weights, a Survey
, 2007
"... Graph labellings form an important graph theory model for the channel assignment problem. An optimum labelling usually depends on one or more parameters that ensure minimum separations between frequencies assigned to nearby transmitters. The study of spans and of the structure of optimum labellings ..."
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Cited by 12 (1 self)
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Graph labellings form an important graph theory model for the channel assignment problem. An optimum labelling usually depends on one or more parameters that ensure minimum separations between frequencies assigned to nearby transmitters. The study of spans and of the structure of optimum labellings as functions of such parameters has attracted substantial attention from researchers, leading to the introduction of real number graph labellings and λgraphs. We survey recent results obtained in this area. The concept of real number graph labellings was introduced a few years ago, and in the sequel, a more general concept of λgraphs appeared. Though the two concepts are quite new, they are so natural that there are already many results on each. In fact, even some older results fall in this area, but their authors used a different mathematical language to state their achievements. Since many of these results are so recent that they are just appearing in various journals, we would like to offer the reader a single reference for the state of art as well as to draw attention to some older results that fall in this area.
Integrated Access Point Placement and Channel Assignment for Wireless LANs in an Indoor Office Environment
"... Abstract — Wireless Local Area Network (WLAN) is currently among the most important technologies for wireless broadband access. The IEEE 802.11 technology is attractive for its maturity and low equipment costs. The overall performance of a specific WLAN installation is largely determined by the netw ..."
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Cited by 9 (0 self)
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Abstract — Wireless Local Area Network (WLAN) is currently among the most important technologies for wireless broadband access. The IEEE 802.11 technology is attractive for its maturity and low equipment costs. The overall performance of a specific WLAN installation is largely determined by the network layout and the radio channels used. Optimizing these design parameters can greatly improve performance. In this paper, access point (AP) placement and channel assignment are optimized using mathematical programming. Traditionally, these decisions are taken sequentially; AP placement is often modeled as a facility location problem, channel assignment as an (extended) graph coloring problem. Treating these key decisions separately may lead to suboptimal designs. We propose an integrated model that addresses both aspects simultaneously aiming at finding a tradeoff between the two optimization objectives. Computational results show that indeed the integrated approach is superior to the sequential one. I.