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Proceedings ArticleDOI

A maximum dispersion approach for rate feasibility problems in SINR model

15 May 2017-pp 1-8
TL;DR: This paper proposes a maximum dispersion based approach for the problem of determining the feasibility of a set of single-hop rates in SINR model and confirms that such an approach performs significantly better than the existing work.
Abstract: In this paper, we propose a maximum dispersion based approach for the problem of determining the feasibility of a set of single-hop rates in SINR model. Recent algorithmic work on capacity maximization has focused on maximizing the number of simultaneously scheduled links. We show that such an approach is not suitable for the problem. We present a polynomial time algorithm to determine the feasibility. We present several simulation results to evaluate the proposed approach. The results confirm that maximum dispersion-based approach is well suited for the problem and that such an approach performs significantly better than the existing work.
References
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Journal ArticleDOI
TL;DR: The stability of a queueing network with interdependent servers is considered and a policy is obtained which is optimal in the sense that its Stability Region is a superset of the stability region of every other scheduling policy, and this stability region is characterized.
Abstract: The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. >

3,018 citations


"A maximum dispersion approach for r..." refers background or methods in this paper

  • ...IV that compare the performance of the proposed algorithm with an optimal algorithm (based on exhaustive search), the algorithm presented in [13] that maximizes the number of simultaneously scheduled links, and a modified version of the max-weight algorithm [21]....

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  • ...We compared the performance of MAX-RATE-GREEDY-DISPERSION with the algorithm of [13], referred here as as MAX-LINKS and a modified version of maximum weight scheduling algorithm [21] described below....

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  • ...Maximum weight scheduling algorithm [21] schedules links essentially in decreasing order of packet queue size in a conflict-free manner....

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Proceedings ArticleDOI
09 Sep 2007
TL;DR: The first NP-completeness proofs in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane, are presented, which proves two problems to be NP-complete: Scheduling and One-Shot Scheduling.
Abstract: In this paper we study the problem of scheduling wireless links in the geometric SINR 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.

430 citations

Proceedings ArticleDOI
22 May 2006
TL;DR: This paper defines and study a generalized version of the SINR model and obtains theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks, and proves that even in worst-case networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm.
Abstract: To date, topology control in wireless ad hoc and sensor networks--the study of how to compute from the given communication network a subgraph with certain beneficial properties .has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical Signal-to-Interference-plus-Noise-Ratio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time.For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worst-case networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graph-based interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.

264 citations

Journal ArticleDOI
TL;DR: This work shows that if the distances do not satisfy the triangle inequality, there is no polynomial-time relative approximation algorithm unless P = NP and proves that obtaining a performance guarantee of less than two is NP-hard.
Abstract: The dispersion problem arises in selecting facilities to maximize some function of the distances between the facilities The problem also arises in selecting nondominated solutions for multiobjective decision making It is known to be NP-hard under two objectives: maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) We consider the question of obtaining near-optimal solutions for MAX-MIN, we show that if the distances do not satisfy the triangle inequality, there is no polynomial-time relative approximation algorithm unless P = NP When the distances satisfy the triangle inequality, we analyze an efficient heuristic and show that it provides a performance guarantee of two We also prove that obtaining a performance guarantee of less than two is NP-hard for MAX-AVG, we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality We also present a polynomial-ti

257 citations


"A maximum dispersion approach for r..." refers methods in this paper

  • ...There exist greedy algorithms that achieve 2-approximation [19], [20]....

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  • ...MAX-RATE-GREEDY-DISPERSION (Algorithm 1) is based on a greedy solution of the max-sum p-dispersion problem [19]....

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Proceedings ArticleDOI
19 Apr 2009
TL;DR: It is shown that maximizing the number of supported connections is NP-hard, even when there is no background noise, in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming.
Abstract: In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported). Our results are: ldr We show that maximizing the number of supported connections is NP-hard, even when there is no background noise. This is in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming. ldr We present a number of approximation algorithms for the problem. All of these approximation algorithms run in polynomial time and have an approximation ratio that is independent of the number of connections. ldr We examine a completely distributed algorithm and analyze it as a game in which a connection receives a positive payoff if it is successful and a negative payoff if it is unsuccessful while transmitting with nonzero power. We show that in this game there is not necessarily a pure Nash equilibrium but if such an equilibrium does exist the corresponding price of anarchy is independent of the number of connections. We also show that a mixed Nash equilibrium corresponds to a probabilistic transmission strategy and in this case such an equilibrium always exists and has a price of anarchy that is independent of the number of connections. This work was supported by NSF contract CCF-0728980 and was performed while the second author was visiting Bell Labs in Summer, 2008.

220 citations