Analysis of Detour Gap Numbers Público

Lou, Siyuan (2012)

Permanent URL: https://etd.library.emory.edu/concern/etds/9s161628x?locale=es
Published

Abstract

Spanner graphs appear in approximation schemes for problems such as the Traveling Salesman Problem, where an edge weighted graph defines a metric on its vertex set. In such schemes, a spanner is a subgraph of the input graph, which still represents nearly the same metric. We bound its total edge weight using the "detour gap number", which is defined by a linear program. In this thesis, we simplify this linear program, and state the complementary slackness conditions relating it and its dual. We also give a way to prune a graph based on those properties and a counter example showing the detour gap number is not monotone under edge deletion. The thesis also introduced a software package to facilitate the calculation of detour gap numbers.

Table of Contents

Content

1 Introduction

2 The Primal Problem

2.1 Simplification

2.2 RunningExample

3 Dual Problem

3.1 ChargingScheme

3.2 RunningExample

4 Combined Primal and Dual

4.1 ComplementarySlackness

4.2 RunningExample

5 Graph Modification

5.1 TreeEdgeContraction

5.2 ParallelEdgeDeletion

6 Nonmonotonicity in Edge Deletion

7 Software

About this Master's Thesis

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Analysis of Detour Gap Numbers () 2018-08-28 11:04:36 -0400

Supplemental Files

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Gap.zip () 2018-08-28 11:07:54 -0400