# Approximate TSP (The Traveling-Salesman Problem)

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## Description

Approximate TSP is the problem of finding an approximate answer to Minimum TSP.

In Minimum TSP, you are given a set $C$ of cities and distances between each distinct pair of cities. The goal is to find an ordering or tour of the cities, such that you visit each city exactly once and return to the origin city, that minimizes the length of the tour. This is the typical variation of TSP.

## Related Problems

Related: Minimum TSP, Maximum TSP

## Parameters

$V$: number of cities (nodes)

$E$: number of roads (edges)

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Applegate et al. | 2006 | $O(V^{2} E)$ | Deterministic | Time | ||

Johnson; D. S.; McGeoch; L. A. | 1997 | $O({2}^{(p(n)$}) | Deterministic | Time | ||

Gutina; Gregory; Yeob; Anders; Zverovich; Alexey | 2002 | - | Deterministic | Time | ||

Rosenkrantz; D. J.; Stearns; R. E.; Lewis; P. M. | 1974 | $O(V^{2})$ | $O({1})$ | 1/2\log n + 1/2 | Deterministic | Time |

Lin–Kernighan | 1981 | $O(V^{2})$ | $O(V)$ | Deterministic | Time & Space | |

Christofides algorithm | 1976 | $O(V^{3})$ | $O(V^{2})$??? | 1.5 | Deterministic | Time |