2-local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs

Šparl, Petra; Žerovnik, Janez

doi:10.1016/j.ipl.2004.02.017

Cited by 24 publications

(16 citation statements)

References 9 publications

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“…Since the channel assignment problem is NP-hard, numerous heuristic schemes have been proposed that come with few, if any, guarantees on performance. Notable exceptions include Sparl and Zerovnik [12], Sudeep and Vishwanathan [13], Janssen et al [14] and Narayanan and Shende [15] who study distributed algorithms for frequency assignment in cellular networks and provide competitive performance bounds. However, this work concentrates on the cellular network case where the graph is always a subgraph of the triangular lattice.…”

Section: Related Workmentioning

confidence: 99%

A Self-Managed Distributed Channel Selection Algorithm for WLANs

Leith

Clifford

2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks

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Abstract-In this paper we consider the problem of a wireless LAN selecting a channel to minimise interference with other WLANs. We focus on interfering infrastructure-mode networks, where each access point (AP) or base station has a wired backhaul link. We introduce a new fully distributed and selfmanaged channel selection algorithm that does not require direct communication between APs nor explicit estimation of the network interference graph. The sole information required by the algorithm is feedback to each WLAN on the presence of interference on a chosen channel; such feedback is already commonly provided by WLAN protocols such as 802.11. We establish that convergence of the distributed algorithm is guaranteed provided that the channel selection problem is feasible. Extensive simulation results are presented that demonstrate rapid convergence under a wide range of network conditions and topologies. While the scope of the present paper is confined to infrastructure networks with static topology, the utility of the proposed algorithm in situations where the network topology is time-varying is briefly discussed.

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Section: Related Workmentioning

confidence: 99%

A Self-Managed Distributed Channel Selection Algorithm for WLANs

Leith

Clifford

2006 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks

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“…But for some various graph classes, this problem may have a better performance. An interesting induced graph, triangle-free hexagonal graph, has been studied for the multicoloring problem [7,16]. A graph is triangle-free if there are no 3-cliques in the graph, i.e., there are no three mutually-adjacent vertices with positive weights.…”

Section: Lemma 1 [8] Let a Be A K-local C-approximate Off-line Algorimentioning

confidence: 99%

“…It is possible to do better for triangle-free hexagonal graphs. For example, in [16], a 2-local 5/4 competitive algorithm was given, and an inductive proof for the 7/6 ratio was reported in [7].…”

Section: Lemma 1 [8] Let a Be A K-local C-approximate Off-line Algorimentioning

confidence: 99%

A 1-Local Asymptotic 13/9-Competitive Algorithm for Multicoloring Hexagonal Graphs

2008

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In the frequency allocation problem, we are given a mobile telephone network, whose geographical coverage area is divided into cells, wherein phone calls are serviced by assigning frequencies to them so that no two calls emanating from the same or neighboring cells are assigned the same frequency. The problem is to use the frequencies efficiently, i.e., minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph. In this paper, we give a 1-local asymptotic 4/3-competitive distributed algorithm for multicoloring a triangle-free hexagonal graph, which is a special case of hexagonal graph. Based on this result, we then propose a 1-local asymptotic 13/9-competitive algorithm for multicoloring the (general-case) hexagonal graph, thereby improving the previous 1-local 3/2-competitive algorithm.

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“…This is a natural choice because it is well known that hexagonal cells provide a coverage with the optimal ratio of the distance between centers compared to the area covered by each cell. Such graphs are called hexagonal graphs [18,19,21]. Indeed, the model is a reasonable approximation for the rural cellular networks where the underlying graph is often nearly planar, and a popular example are the sets of benchmark problems based on the real cellular network around Philadelphia [2] (see the FAP website [29]).…”

Section: Introductionmentioning

confidence: 99%

“…McDiarmid and Reed proved in [12] that multicoloring of hexagonal graphs is NP-complete. In the last decade there were several results on upper bounds for the multichromatic number in terms of weighted clique number for hexagonal graphs, some of which also provide approximation algorithms that are fully distributed and run in constant time [8,9,10,12,13,14,16,18,19,20,15,21,23,24,25,27]. The best known approximation ratios are χ m (G) ≤ (4/3)ω(G) + O(1) in general [12,14,18] and χ m (G) ≤ (7/6)ω(G)+O(1) for triangle free hexagonal graphs [8,15,16] [12].…”

Section: Introductionmentioning

confidence: 99%