Location Oblivious Distributed Unit Disk Graph Coloring

Couture, Mathieu; Barbeau, Michel; Bose, Prosenjit; Carmi, Paz; Kranakis, Evangelos

doi:10.1007/978-3-540-72951-8_18

Cited by 6 publications

(3 citation statements)

References 9 publications

(12 reference statements)

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“…The performance ratio of our algorithms is bounded by C(1 + 2z 1 z 2 ) A . Efficient distributed algorithms are known for coloring unit-disc graphs in the plane [10] and more generally bounded-independence graphs [34]. Thus, our characterization can be translated into distributed constant-factor approximation algorithms of PC-Scheduling and PC-Capacity in nearly-equilength linksets, when given the appropriate communication primitives.…”

Section: Definition 33mentioning

confidence: 99%

Wireless Scheduling with Power Control

Halldórsson

2009

Lecture Notes in Computer Science

114

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We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints.We give an algorithm that attains an approximation ratio of O(log n · log log Λ), where Λ is the ratio between the longest and the shortest linklength. Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)-approximation. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We show this dependence on Λ to be unavoidable, giving a construction for which any oblivious power assignment results in a Ω(log log Λ)-approximation.We also give a simple online algorithm that yields a O(log Λ)-approximation, by a reduction to the coloring of unit-disc graphs. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics.

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Section: Definition 33mentioning

confidence: 99%

Wireless Scheduling with Power Control

Halldórsson

2009

Lecture Notes in Computer Science

114

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“…Efficient distributed algorithms are known for coloring unit-disc graphs in the plane [Couture et al 2007] and more generally bounded-independence graphs . Thus, our characterization can be translated into distributed constant-factor approximation algorithms of PC-Scheduling and PC-Capacity in nearly equilength linksets, when given the appropriate communication primitives.…”

Section: Theorem 38 Let L Be a Nearly Equilength Linkset Let S Be mentioning

confidence: 99%

Wireless scheduling with power control

Halldórsson

2012

ACM Trans. Algorithms

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We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints.We give an algorithm that attains an approximation ratio of O(log n · log log ), where n is the number of links and is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on is unavoidable, showing that any reasonably behaving oblivious power assignment results in a (log log )-approximation.These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.

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“…Our algorithm allows to conclude that no such tradeoff is necessary. These results were presented at SIROCCO 2007 [22].…”

Section: Overview Of Resultsmentioning

confidence: 94%