Link scheduling in polynomial time

Hajek, Bruce; Sasaki, Galen H.

doi:10.1109/18.21215

Cited by 486 publications

(345 citation statements)

References 11 publications

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“…A variety of centralized and decentralized approximation algorithms have been proposed and their quality analyzed for this kind of model [14,20,24,31,32]. Most recently, Brar et al [5] present a scheduling method that is based on a greedy assignment of weighted colors.…”

Section: Related Workmentioning

confidence: 99%

Complexity in geometric SINR

Goussevskaia

Oswald

Wattenhofer

2007

Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing

347

363

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In this paper we study the problem of scheduling wireless links in the geometric SIN R model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NP-completeness proofs in such a model. In particular, we prove two problems to be NP-complete: Scheduling and One-Shot Scheduling. The first problem consists in finding a minimum-length schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximum-weight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.

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Section: Related Workmentioning

confidence: 99%

Complexity in geometric SINR

Goussevskaia

Oswald

Wattenhofer

2007

Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing

347

363

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“…Computing the probability vector p that attains the above delay guarantee requires finding the weights {w k } from the arrival vector λ, and finding the chromatic number of the interference graph. The rate decomposition problem to calculate the independent set weights {w k } is not known to be polynomially solvable in the general case; in presence of primary interference constraints only (i.e., if two links can transmit together successfully as long as they do not have any common end node), this problem can be solved in polynomial time [10]. Finding the chromatic number requires solving a graph coloring problem, which is NP-hard [3].…”

Section: Upper Bounds On Expected Delaymentioning

confidence: 99%

Delay Guarantees for Throughput-Optimal Wireless Link Scheduling

Kar

Sarkar

Ghavami

et al. 2012

IEEE Trans. Automat. Contr.

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Abstract-We consider the question of obtaining tight delay guarantees for throughout-optimal link scheduling in arbitrary topology wireless ad-hoc networks. We consider two classes of scheduling policies: 1) a maximum queue-length weighted independent set scheduling policy, and 2) a randomized independent set scheduling policy where the independent set scheduling probabilities are selected optimally. Both policies stabilize all queues for any set of feasible packet arrival rates, and are therefore throughput-optimal. For these policies and i.i.d. packet arrivals, we show that the average packet delay is bounded by a constant that depends on the chromatic number of the interference graph, and the overall load on the network. We also prove that this upper bound is asymptotically tight in the sense that there exist classes of topologies where the expected delay attained by any scheduling policy is lower bounded by the same constant. Through simulations we examine the scaling of the average packet delay with respect to the overall load on the network, and the chromatic number of the link interference graph.

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“…Hajek and Sasaki [8] investigate the schedulability of a routing in polynomial time. Kodialam and Nandagopal [12] give necessary and sufficient conditions implicitly in [8]. These conditions are expressed as linear constraints over the flows and data rate on neighboring edges of a node.…”

Section: F Schedulabilitymentioning

confidence: 99%

“…Recently there is increased interest in jointly considering routing and scheduling. Schedulability of a routing is studied in Hajek and Sasaki [8] and Kodialam and Nandagopal [12] for the "free of secondary interference" model, where a node can transmit to or receive from at most one node. Necessary and sufficient conditions are derived.…”

Section: Introductionmentioning

confidence: 99%

Optimal Traffic-Oblivious Energy-Aware Routing for Multihop Wireless Networks

Li¹,

Harms²,

Holte³

2006

Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications

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Abstract-Energy efficiency is an important issue in multihop wireless networks with energy concerns. Usually it is achieved with accurate knowledge of the traffic pattern and/or the current network information such as the remaining energy level. We investigate the problem of designing a routing scheme to minimize the maximum energy utilization of a multihop wireless network with weak assumption of the traffic pattern and without ongoing collection of network information. We develop polynomial size LP models to design such a routing scheme. We discuss generalizations of the LP models to various radio transmission models. In an interference-limited scenario, we show how to guarantee schedulability of the oblivious routing. We present an extension to consider lossy links. We also discuss implementation issues. The LP models achieve performance close to what an oracle can achieve in the performance study. The results for multihop wireless networks with a single sink are especially good. We make a first stride in designing a traffic-oblivious energy-aware routing framework in multihop wireless networks.

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Link scheduling in polynomial time

Cited by 486 publications

References 11 publications

Complexity in geometric SINR

Complexity in geometric SINR

Delay Guarantees for Throughput-Optimal Wireless Link Scheduling

Optimal Traffic-Oblivious Energy-Aware Routing for Multihop Wireless Networks

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