The minimum latency problem

Blum, Avrim; Chalasani, Prasad; Coppersmith, Don; Pulleyblank, Bill; Raghavan, Prabhakar; Sudan, Madhu

doi:10.1145/195058.195125

Cited by 233 publications

(209 citation statements)

References 10 publications

(5 reference statements)

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“…In this section, we first give a simple example that shows that OffNNA does not necessarily traverse every edge of a star only a constant number of times -even if the graph is linear, a special case of a star topology. Then we show that, nevertheless, L OffNNA s; W; G ,1 has been traversed 2 N times, which is not a constant [3]. We defer the proof of the theorem to the appendix because it contains quite a few technicalities.…”

Section: Graphs With Linear or Star Topologymentioning

confidence: 90%

Graph learning with a nearest neighbor approach

Koenig

Smirnov

1996

Proceedings of the Ninth Annual Conference on Computational Learning Theory - COLT '96

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In this paper, we study how to traverse all edges of an unknown graph G = V;E that is bi-directed and strongly connected. This problem can be solved with a simple algorithm that traverses all edges at most twice, and no algorithm can do better in the worst case. Artificial Intelligence researchers, however, often use the following online nearest neighbor algorithm: "repeatedly take a shortest path to the closest unexplored edge and traverse it." We prove bounds on the worst-case complexity of this algorithm. We show, for example, that its worst-case complexity is close to optimal for some classes of graphs, such as graphs with linear or star topology and dense graphs with edge lengths one. In general, however, its complexity can grow faster than linear in the sum of all edge lengths, although not faster than logV times the sum of all edge lengths.

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Section: Graphs With Linear or Star Topologymentioning

confidence: 90%

Graph learning with a nearest neighbor approach

Koenig

Smirnov

1996

Proceedings of the Ninth Annual Conference on Computational Learning Theory - COLT '96

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“…Our algorithm is based on algorithms for the deterministic TRP [3,4,8]. However, the a priori setting makes the problem a lot harder to solve.…”

Section: Lemma 1 For Any Tour and Vertex I We Have C I ≥ D(r I)mentioning

confidence: 99%

“…As explained above, even the problem on the line is non-trivial in the a priori setting and is not known to be solvable in polynomial time. Our algorithm makes use of an (α, β)-TSP-approximator in the a priori setting, which is similar to the one introduced in [3]. Suppose we have an instance of a priori TSP and a number L. The goal is to find a tour of expected length at most L which minimizes the number of unvisited vertices.…”

Section: Lemma 1 For Any Tour and Vertex I We Have C I ≥ D(r I)mentioning

confidence: 99%

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The A Priori Traveling Repairman Problem

Sitters

2017

Algorithmica

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The field of a priori optimization is an interesting subfield of stochastic combinatorial optimization that is well suited for routing problems. In this setting, there is a probability distribution over active sets, vertices that have to be visited. For a fixed tour, the solution on an active set is obtained by restricting the solution on the active set. In the well-studied a priori traveling salesman problem, the goal is to find a tour that minimizes the expected length. In the a priori traveling repairman problem (TRP), the goal is to find a tour that minimizes the expected sum of latencies. In this paper, we study the uniform model, where a vertex is in the active set with probability p independently of the other vertices, and give the first constant-factor approximation for a priori TRP.

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“…To do this, we use the following corollary (in [BCC+94]) to a result by Goemans and Williamson [GW92]. In [BCC+94] this is called a (3,6)-TSP approximator.…”

Section: Connect Together All the Components Found Inmentioning

confidence: 99%

Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen

Awerbuch

Azar

Blum

et al. 1995

Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing - STOC '95

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Consider a salesperson that must sell some quota of brushes in order to win a trip to Hawaii. This salesperson has a map (a weighted graph) in which each city has an attached demand specifying the number of brushes that can be sold in that city. What is the best route to take to sell the quota while traveling the least distance possible? Notice that unlike the standard traveling salesman problem, not only do we need to figure out the order in which to visit thE cities, but we must decide the more fundamental question: which cities do we want to visit? In this paper we give the first approximation algorithms with poly-logar. rhmic performance guarantees for this problem, as well as for the slightly more general PCTSP problem of Balas.

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The minimum latency problem

Cited by 233 publications

References 10 publications

Graph learning with a nearest neighbor approach

Graph learning with a nearest neighbor approach

The A Priori Traveling Repairman Problem

Improved approximation guarantees for minimum-weight k-trees and prize-collecting salesmen

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