Packet Routing: Complexity and Algorithms

Peis, Britta; Skutella, Martin; Wiese, Andreas

doi:10.1007/978-3-642-12450-1_20

Cited by 22 publications

(27 citation statements)

References 29 publications

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“…Here we extend the selfish routing model by incorporating a temporal component into the problem formulation. Other attempts to address this issue include [21,19,13,24], but none of these results discuss coordination mechanisms using strongly local (decentralized) policies.…”

Section: Our Contributions and Techniquesmentioning

confidence: 99%

“…However they lack an important aspect of real network routing which is the fact that routing happens over time, and any realistic model should take this into account. To address this issue, several new models have been proposed to capture the nature of realistic routing over time [10,11,21,19,24,13,12,4]. Amongst these models, the concept of coordination mechanisms, first introduced in an influential paper by Christodoulou, Koutsoupias, and Nanavati [10], have been proposed to capture the queueing nature of routing.…”

Section: Introductionmentioning

confidence: 99%

“…The sojourn time of a job is defined as the total time the job spends in the network. On the other hand, minimizing the makespan of a schedule, defined as the maximum sojourn time over all the jobs, has a vast literature in these settings [14,25,24], including the celebrated result of Leighton, Maggs and Rao [22].…”

Section: Introductionmentioning

confidence: 99%

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Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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Abstract. While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first coordination mechanisms with provable price of anarchy for this problem. Interestingly, we achieve our price of anarchy results using simple and strongly local policies such as Shortest Job First and the Smith's Rule (also called HDF). In particular, for the case of unweighted jobs, we design a coordination mechanism with polylogarithmic price of anarchy. For weighted jobs, on the other hand, we show that price of anarchy is a function of the depth of the tree and accompany this result by a lower bound for the price of anarchy for the Smith Rule policy and other common strongly local scheduling policies. Our price of anarchy results also imply improved approximation algorithms for the underlying optimization problem of routing over a tree. This problem is well motivated from applications of routing in supercomputers and data center networks where average sojourn time is an important metric.

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Section: Our Contributions and Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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“…We refer to such convoys as point convoys or particle convoys. Non-zero convoy lengths provide a sharp point of distinction between CMP problems that arise in physical distribution and logistics vis-à-vis other similar problems that arise in packet routing in telecommunication networks (Peis et al 2010;Di Ianni 1998). 2.…”

Section: Introductionmentioning

confidence: 99%

Computational complexity of convoy movement planning problems

Gopalan

2015

Math Meth Oper Res

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Convoy movement planning problems arise in a number of important logistical contexts, including military planning, railroad optimization and automated guided vehicle routing. In the convoy movement problem (CMP), a set of convoys, with specified origins and destinations, are to be routed with the objective of minimizing either makespan or total flow time, while observing a number of side constraints. This paper characterizes the computational complexity of several restricted classes of CMPs. The principal objective is to identify the most parsimonious set of problem features that make the CMP intractable. A polynomial-time algorithm is provided for the single criterion two-convoy movement problem. The performance of a simple prioritizationidling approximation algorithm is also analyzed for the K-convoy movement problem. Error bounds are developed for the makespan and flow time objectives.

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“…Many applications, however, require a time dimension to be considered: instead of a picture of the network at one instant, we need to consider a video of the network flow over a period of time. These applications arise from various fields of studies, including transportation [14], evacuation planning [23,12], job scheduling [2], electronic communication [5,16], network routing [18,3,19], and parallel computing [15]. Such a requirement leads to the dynamic network flow model [8,4,13].…”

Section: Introductionmentioning

confidence: 99%

On the Quickest Flow Problem in Dynamic Networks – A Parametric Min-Cost Flow Approach

Lin¹,

Jaillet²

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider the quickest flow problem in dynamic networks with a single source s and a single sink t: given an amount of flow F , find the minimum time needed to send it from s to t, and the corresponding optimal flow over time.We introduce new mathematical formulations and derive optimality conditions for the quickest flow problem. Based on the optimality conditions, we develop a new costscaling algorithm that leverages the parametric nature of the problem. The algorithm solves the quickest flow problem with integer arc costs in O(nm log(n 2 /m) log(nC)) time, where n, m, and C are the number of nodes, arcs, and the maximum arc cost, respectively.Our algorithm runs in the same time bound as the costscaling algorithm by Goldberg and Tarjan [10,11] for solving the min-cost flow problem. This result shows for the first time that the quickest flow problem can be solved within the same time bound as one of the fastest algorithms for the min-cost flow problem. As a consequence, our algorithm will remain one of the fastest unless the quickest flow problem can be shown to be simpler than the min-cost flow problem.

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Packet Routing: Complexity and Algorithms

Cited by 22 publications

References 29 publications

Coordination Mechanisms for Selfish Routing over Time on a Tree

Coordination Mechanisms for Selfish Routing over Time on a Tree

Computational complexity of convoy movement planning problems

On the Quickest Flow Problem in Dynamic Networks – A Parametric Min-Cost Flow Approach

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