A method for obtaining the maximum multiroute flows in a network

Kishimoto, Wataru

doi:10.1002/(sici)1097-0037(199607)27:4<279::aid-net3>3.0.co;2-d

Cited by 47 publications

(58 citation statements)

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“…What is the maximum time for which this network can provide 2-barrier coverage? We provide a provably optimal solution to this problemby making use of multiroute network flows [19]. We begin with some assumptions and definitions.…”

Section: A Upper Bound On Network Lifetimementioning

confidence: 99%

“…If we can devise a method to determine the maximum value of a composite k-flow in a G L (N ), then we can derive an upper bound on the network lifetime achievable by N . For this purpose, we make use of the MEM algorithm [19].…”

Section: Definition 44: Basic K-flow Of Value a A Set Of K Nodedisjmentioning

confidence: 99%

“…The Prahari algorithm first invokes the MEM algorithm [19] to determinef , the maximum value of composite k-flow in G L (N ). Let F M EM (N ) be the flow network resulting from this step.…”

Section: B Achieving the Upper Boundmentioning

confidence: 99%

“…Alternatively, if the flow network F M EM (N ) is such that some node in V − {s, t} has an indegree or outdegree of more than 2, then the Prahari algorithm invokes the SEM algorithm from [19] to decompose the flow network into α > k basic k-flows. SEM then merges identical basic k-flows into a single aggregate basic k-flow.…”

Section: B Achieving the Upper Boundmentioning

confidence: 99%

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Maximizing the Lifetime of a Barrier of Wireless Sensors

Kumar

Lai

Posner³

et al. 2010

IEEE Trans. on Mobile Comput.

104

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Abstract-To make a network last beyond the lifetime of an individual sensor, redundant sensors must be deployed. What sleep-wakeup schedule can then be used for individual sensors so that the redundancy is appropriately exploited to maximize the network lifetime?We develop optimal solutions to both problems for the case when wireless sensors are deployed to form an impenetrable barrier for detecting movements. In addition to being provably optimal, our algorithms work for non-disk sensing regions and heterogeneous sensing regions. Further, we provide an optimal solution for the more difficult case when the lifetimes of individual sensors are not equal.Developing optimal algorithms for both homogeneous and heterogeneous lifetimes allows us to obtain by simulation several interesting results. We show that even when an optimal number of sensors have been deployed randomly, statistical redundancy can be exploited to extend the network lifetime by up to seven times. We also use simulation to show that the assumption of homogeneous lifetime can result in severe loss (two-thirds) of the network lifetime. Although these results are specifically for barrier coverage, they provide an indication of behavior for other coverage models.Index Terms-Wireless sensor networks, sleep-wakeup, sensor deployment, barrier coverage, multi-route network flows.

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Section: A Upper Bound On Network Lifetimementioning

confidence: 99%

Section: Definition 44: Basic K-flow Of Value a A Set Of K Nodedisjmentioning

confidence: 99%

“…The Prahari algorithm first invokes the MEM algorithm [19] to determinef , the maximum value of composite k-flow in G L (N ). Let F M EM (N ) be the flow network resulting from this step.…”

Section: B Achieving the Upper Boundmentioning

confidence: 99%

Section: B Achieving the Upper Boundmentioning

confidence: 99%

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Maximizing the Lifetime of a Barrier of Wireless Sensors

Kumar

Lai

Posner³

et al. 2010

IEEE Trans. on Mobile Comput.

104

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“…A flow of size M between two vertices is h-balanced if the flow on every edge is at most M/h. Clearly, every h-route flow is an h-balanced flow; the opposite (less obvious) claim is also true: Every h-balanced (acyclic) flow is an h-route flow [1,6,21].…”

Section: Flows Multiroute Flows and Cutsmentioning

confidence: 99%

Untitled

Bruhn¹,

Černý²,

Hall³

et al. 2007

ToC

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Abstract:For an integer h ≥ 1, an elementary h-route flow is a flow along h edge disjoint paths between a source and a sink, each path carrying a unit of flow, and a single commodity h-route flow is a non-negative linear combination of elementary h-route flows. An instance of a single source multicommodity flow problem for a graph G = (V, E) consists of a source vertex s ∈ V and k sinks t 1 , . . . ,t k ∈ V corresponding to k commodities; we denote it I = (s;t 1 , . . . ,t k ). In the single source multicommodity multiroute flow problem, we are given an instance I = (s;t 1 , . . . ,t k ) and an integer h ≥ 1, and the objective is to maximize the * A preliminary version of this work appeared in

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On multiroute maximum flows in networks

Aggarwal

Orlin

2001

Networks

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Let G = (N, A) be a network with a designated source node s, a designated sink node t, and a finite integral capacity uij on each arc (i, j) ∈ A. An elementary K‐flow is a flow of K units from s to t such that the flow on each arcis 0 or 1. A K‐route flow is a flow from s to t that may be expressed as a nonnegative linear sum of elementary K‐flows. In this paper, we show how to determine a maximum K‐route flow as a sequence of O(min {log (nU), K}( maximum‐flow problems. This improves upon the algorithm by Kishimoto, which solves this problem as a sequence of K maximum‐flow problems. In addition, we have simplified and extended some of the basic theory. We also discuss the application of our technique to Birkhoff's theorem and a scheduling problem. © 2001 John Wiley & Sons, Inc.

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A method for obtaining the maximum multiroute flows in a network

Cited by 47 publications

References 0 publications

Maximizing the Lifetime of a Barrier of Wireless Sensors

Maximizing the Lifetime of a Barrier of Wireless Sensors

Untitled

On multiroute maximum flows in networks

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