On M-route flows in a network

Kishimoto, Wataru; Takeuchi, Masashi

doi:10.1109/iccs.1992.255031

Cited by 23 publications

(28 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a proof of the correctness of the SEM algorithm, we refer the reader to [23]. Since each basic flow N i provides k-barrier coverage for f (N i )/k time units and…”

mentioning

confidence: 99%

Maximizing the Lifetime of a Barrier of Wireless Sensors

Kumar

Lai

Posner³

et al. 2010

IEEE Trans. on Mobile Comput.

104

View full text Add to dashboard Cite

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.

show abstract

“…For a proof of the correctness of the SEM algorithm, we refer the reader to [23]. Since each basic flow N i provides k-barrier coverage for f (N i )/k time units and…”

mentioning

confidence: 99%

Maximizing the Lifetime of a Barrier of Wireless Sensors

Kumar

Lai

Posner³

et al. 2010

IEEE Trans. on Mobile Comput.

104

View full text Add to dashboard Cite

show abstract

“…The concept of multi-route flows was introduced by Kishimoto and Takeuchi [12]. The problem of finding a maximum (multicommodity) multi-route flow can be formulated using linear programming and is solvable in polynomial time.…”

Section: Related Resultsmentioning

confidence: 99%

“…An elementary h-route flow, for an integer h ≥ 1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow [12,3] is a nonnegative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal disconnects a given source-sink pair with respect to h-route flows (in the multicommodity setting, it disconnects every source-sink pair).…”

Section: Introductionmentioning

confidence: 99%

Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

Kolman

Scheideler

2013

Theory Comput Syst

View full text Add to dashboard Cite

An elementary h-route flow, for an integer h ≥ 1, is a set of h edge-disjoint paths between a source and a sink, each path carrying a unit of flow, and an h-route flow is a non-negative linear combination of elementary h-route flows. An h-route cut is a set of edges whose removal decreases the maximum h-route flow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and flows, for h ≤ 3: The size of a minimum h-route cut is at least f /h and at most O(log 4 k · f ) where f is the size of the maximum h-route flow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log 4 k). Previously, polylogarithmic approximation was known only for h-route cuts for h ≤ 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity flows and cuts. Similar results are shown also for the sparsest multiroute cut problem.

show abstract

“…Here we propose a less aggressive approach using M-Route flow algorithm to compute the lower bound. We would suggest interested readers to refer [16] for definition of M-Route flow. To define loosely, M-Route flow is any flow that can be expressed as a non-negative linear sum of elementary MFlows.…”

Section: Mixed Bound Abstraction Schemementioning

confidence: 99%

“…To define loosely, M-Route flow is any flow that can be expressed as a non-negative linear sum of elementary MFlows. [16] Defines M-Route flow in the context of both edge and vertex disjoint paths. For our study we use the theory of M-Route edge flows.…”

Section: Mixed Bound Abstraction Schemementioning

confidence: 99%

A Dynamic Managed VPN Service: Architecture And Algorithms

Ravindran

Huang

2006

2006 IEEE International Conference on Communications

View full text Add to dashboard Cite

Abstract-VPN as a managed service enables the service provider to offer more demanding and revenue generating services. Some of the more common managed VPN services known today include auto discovery, security and also a potential ability to perform on demand signaling. In this paper we try to tackle an important problem of service providers providing bandwidth service on demand on an IP/MPLS core network. We propose a managed VPN architecture for such a service highlighting the novelty in our architecture. We concentrate on an important aspect of service definition called the topology abstraction service and define a new problem called the VPN core capacity sharing problem that arises in this context. We propose three schemes to solve this problem borrowing established results from graph theory. As part of our simulation study, we evaluate each of these strategies with different call arrival scenarios and present their results.

show abstract

On M-route flows in a network

Cited by 23 publications

References 2 publications

Maximizing the Lifetime of a Barrier of Wireless Sensors

Maximizing the Lifetime of a Barrier of Wireless Sensors

Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing

A Dynamic Managed VPN Service: Architecture And Algorithms

Contact Info

Product

Resources

About