On the single-source unsplittable flow problem

Dinitz, Yefim; Garg, Naveen; Goemans, Michel X.

doi:10.1109/sfcs.1998.743461

Cited by 60 publications

(111 citation statements)

References 6 publications

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“…Dinitz et al [10] present an algorithm that achieves an approximation factor of ρ = 1/5 in running time O(KM (K + M )), using ideas by Kolliopoulos and Stein [19]. Therefore the solution we get for our problem has a guaranteed worst-case performance of at least 1/10 of the optimum.…”

Section: The Case µmentioning

confidence: 95%

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Maximizing Throughput in Queueing Networks with Limited Flexibility

Down

Karakostas

2006

LATIN 2006: Theoretical Informatics

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We study a queueing network where customers go through several stages of processing, with the class of a customer used to indicate the stage of processing. The customers are serviced by a set of flexible servers, i.e., a server is capable of serving more than one class of customers and the sets of classes that the servers are capable of serving may overlap. We would like to choose an assignment of servers that achieves the maximal capacity of the given queueing network, where the maximal capacity is λ * if the network can be stabilized for all arrival rates λ < λ * and cannot possibly be stabilized for all λ > λ * . We examine the situation where there is a restriction on the number of servers that are able to serve a class, and reduce the maximal capacity objective to a maximum throughput allocation problem of independent interest: the Total Discrete Capacity Constrained Problem (TDCCP). We prove that solving TDCCP is in general NP-complete, but we also give exact or approximation algorithms for several important special cases and discuss the implications for building limited flexibility into a system.

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Section: The Case µmentioning

confidence: 95%

“…We will denote this first algorithm as Algorithm 1. It is the combination of the algorithm of [6] with the algorithm of [10], and goes through the following stages:…”

Section: The Case µmentioning

confidence: 99%

Maximizing Throughput in Queueing Networks with Limited Flexibility

Down

Karakostas

2006

LATIN 2006: Theoretical Informatics

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“…Dinitz, Garg, and Goemans [4] present an algorithm that turns a given splittable flow f init satisfying demands d i , i = 1, . .…”

Section: Introductionmentioning

confidence: 99%

“…The demand of each commodity must be routed along a single path. In a groundbreaking paper Dinitz, Garg, and Goemans [4] prove that any given (splittable) flow satisfying certain demands can be turned into an unsplittable flow with the following nice property: In the unsplittable flow, the flow value on any arc exceeds the flow value on that arc in the given flow by no more than the maximum demand.Goemans conjectures that this result even holds in the more general context with arbitrary costs on the arcs when it is required that the cost of the unsplittable flow must not exceed the cost of the given (splittable) flow. The following is an equivalent formulation of Goemans' conjecture: Any (splittable) flow can be written as a convex combination of unsplittable flows such that the unsplittable flows have the nice property mentioned above.…”

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Convex Combinations of Single Source Unsplittable Flows

Martens

Salazar

Skutella

Algorithms – ESA 2007

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Abstract. In the single source unsplittable flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given digraph. The demand of each commodity must be routed along a single path. In a groundbreaking paper Dinitz, Garg, and Goemans [4] prove that any given (splittable) flow satisfying certain demands can be turned into an unsplittable flow with the following nice property: In the unsplittable flow, the flow value on any arc exceeds the flow value on that arc in the given flow by no more than the maximum demand.Goemans conjectures that this result even holds in the more general context with arbitrary costs on the arcs when it is required that the cost of the unsplittable flow must not exceed the cost of the given (splittable) flow. The following is an equivalent formulation of Goemans' conjecture: Any (splittable) flow can be written as a convex combination of unsplittable flows such that the unsplittable flows have the nice property mentioned above. We prove a slightly weaker version of this conjecture where each individual unsplittable flow occurring in the convex combination does not necessarily fulfill the original demands but rounded demands. Preliminary computational results based on our underlying algorithm support the strong version of the conjecture.

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The building evacuation problem with shared information

Chen

Miller-Hooks

2008

Naval Research Logistics

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Abstract:In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP-hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real-world network representing a four-story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided.

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On the single-source unsplittable flow problem

Cited by 60 publications

References 6 publications

Maximizing Throughput in Queueing Networks with Limited Flexibility

Maximizing Throughput in Queueing Networks with Limited Flexibility

Convex Combinations of Single Source Unsplittable Flows

The building evacuation problem with shared information

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