LNCS 2748 The Traveling Salesman Problem for Cubic Graphs 1st Edition by David Eppstein ISBN 3540450785 9783540450788

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Product details:

ISBN 10: 3540450785

ISBN 13: 9783540450788

Author: David Eppstein 

LNCS 2748 – The Traveling Salesman Problem for Cubic Graphs 1st Edition: We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time <span id="MathJax-Element-1-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; font-size-adjust: none; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="O(2n/3)≈1.25992n”>O(2n/3)≈1.25992n and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound, and count the number of Hamiltonian cycles in time <span id="MathJax-Element-2-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; font-size-adjust: none; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="O(23n/8nO(1))≈1.29684n”>O(23n/8nO(1))≈1.29684n. We also solve the traveling salesman problem in graphs of degree at most four, by a randomized (Monte Carlo) algorithm with runtime <span id="MathJax-Element-3-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; font-size-adjust: none; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="O((27/4)n/3)≈1.88988n”>O((27/4)n/3)≈1.88988n. Our algorithms allow the input to specify a set of forced edges which must be part of any generated cycle.

 

LNCS 2748 – The Traveling Salesman Problem for Cubic Graphs 1st Edition Table of contents:

1 Introduction

2 The Algorithm and its Correctness

3 Implementation Details

4 Analysis

5 Degree Four

6 Listing All Hamiltonian Cycles

7 Graphs with Many Hamiltonian Cycles

 

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