Submodularity and the traveling salesman problem

Yale T. Herer

doi:10.1016/S0377-2217(98)00175-1

Submodularity and the traveling salesman problem

Yale T. Herer

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we investigate the relationship between traveling salesman tour lengths and submodular functions. This work is motivated by the one warehouse multi-retailer inventory/distribution problem with traveling salesman tour vehicle routing costs. Our goal is to find a submodular function whose values are close to those of optimal tour lengths through a central warehouse and a group of retailers. Our work shows that a submodular approximation to traveling salesman tour lengths whose error is bounded by a constant does not exist. However, we present heuristics that have errors which grow slowly with the number of retailers for the traveling salesman problem in the Euclidean plane. Furthermore, we perform computational tests that show that our submodular approximations of traveling salesman tour lengths have smaller errors than our theoretical worst case analysis would lead us to believe.

Original language	English
Pages (from-to)	489-508
Number of pages	20
Journal	European Journal of Operational Research
Volume	114
Issue number	3
DOIs	https://doi.org/10.1016/S0377-2217(98)00175-1
State	Published - 1 May 1999

Keywords

Submodular functions
Traveling salesman

ASJC Scopus subject areas

General Computer Science
Modeling and Simulation
Management Science and Operations Research
Information Systems and Management

Access to Document

10.1016/S0377-2217(98)00175-1

Cite this

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title = "Submodularity and the traveling salesman problem",

abstract = "In this paper we investigate the relationship between traveling salesman tour lengths and submodular functions. This work is motivated by the one warehouse multi-retailer inventory/distribution problem with traveling salesman tour vehicle routing costs. Our goal is to find a submodular function whose values are close to those of optimal tour lengths through a central warehouse and a group of retailers. Our work shows that a submodular approximation to traveling salesman tour lengths whose error is bounded by a constant does not exist. However, we present heuristics that have errors which grow slowly with the number of retailers for the traveling salesman problem in the Euclidean plane. Furthermore, we perform computational tests that show that our submodular approximations of traveling salesman tour lengths have smaller errors than our theoretical worst case analysis would lead us to believe.",

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author = "Herer, {Yale T.}",

note = "Funding Information: This work was supported in part by NSF grants ECS-8404641 and DMC-8451984, by AT&T Information Systems and DuPont Corporation, and by The Fund for the Promotion of Research at the Technion. ",

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Submodularity and the traveling salesman problem

Abstract

Keywords

ASJC Scopus subject areas

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