# An Exact Algorithm for TSP in Degree-3 Graphs Via Circuit Procedure and Amortization on Connectivity Structure

@article{Xiao2015AnEA, title={An Exact Algorithm for TSP in Degree-3 Graphs Via Circuit Procedure and Amortization on Connectivity Structure}, author={Mingyu Xiao and Hiroshi Nagamochi}, journal={Algorithmica}, year={2015}, volume={74}, pages={713-741} }

The paper presents an $$O^*(1.2312^n)$$O∗(1.2312n)-time and polynomial-space algorithm for the traveling salesman problem in an $$n$$n-vertex graph with maximum degree 3. This improves all previous time bounds of polynomial-space algorithms for this problem. Our algorithm is a simple branch-and-search algorithm with only one branch rule designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce…

## 16 Citations

### A Polynomial-Space Exact Algorithm for TSP in Degree-6 Graphs

- Computer Science, MathematicsJCDCGG
- 2015

This paper presents the first polynomial-space exact algorithm specialized for the TSP in graphs with degree at most 6. We develop a set of branching rules to aid the analysis of the branching…

### A POLYNOMIAL-SPACE EXACT ALGORITHM FOR TSP IN DEGREE-5 GRAPHS

- Computer Science
- 2015

This work presents a polynomial-space branching algorithm for the TSP in graphs with degree at most 5, and shows that it has a running time of O (2.4723 n ), which is the first exact algorithm specialized to graphs of such high degree.

### An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

- Computer ScienceJ. Inf. Process.
- 2017

A polynomial-space branching algorithm for the TSP in an n-vertex graph with degree at most 5 is presented, and it is shown that it has a running time of O∗(2.3500n), which improves the previous best known time bound of O ∗( 2.4723n) given by the authors.

### An Improved Exact Algorithm for TSP in Graphs of Maximum Degree 4

- Computer ScienceTheory of Computing Systems
- 2015

The paper presents a 1.692nnO(1)-time polynomial-space algorithm for the traveling salesman problem in an n-vertex edge-weighted graph with maximum degree 4, which improves the previous results of…

### The Asymmetric Travelling Salesman Problem in Sparse Digraphs

- Computer ScienceIPEC
- 2020

Two new deterministic algorithms for ATSP are presented: the first running in time $O(2^{0.441(d-1)n})$ and polynomial space, and the second in exponential space with running time of $O^*(\tau(d)^{n/2})$ for a function $\t Tau(d)\le d$.

### An iterative algorithm to eliminate edges for traveling salesman problem based on a new binomial distribution

- Computer ScienceApplied Intelligence
- 2018

A previous probability model for the optimal Hamiltonian cycle edges according to the frequency quadrilaterals in Kn$K_{n}$ is updated to show the probability that an edge e has the frequency 5 in a frequency quadrilateral.

### Exact and Approximate Algorithms for Computing a Second Hamiltonian Cycle

- Computer Science, MathematicsMFCS
- 2020

A linear-time algorithm computing a second cycle with length at least $n - 4\alpha (\sqrt{n}+2\alpha)+8$ where $\alpha = \frac{\Delta-2}{\delta-2}$ and $\delta,\Delta$ are the minimum and the maximum degree of the graph, respectively is provided.

### Wang An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem

- Computer Science
- 2018

An improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals is presented, enhanced by adjusting two parameters of the algorithm.

### An Improved Method to Compute Sparse Graphs for Traveling Salesman Problem

- Computer Science
- 2018

An improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals is presented, enhanced by adjusting two parameters of the algorithm.

### A Heuristic Algorithm to Compute a Subgraph for TSP Based on Frequency Quadrilaterals

- Computer Science
- 2021

A heuristic algorithm was presented to compute certain subgraphs for symmetric traveling salesman problem using frequency quadrilaterals and illustrated that in certain instances for Euclidean TSP with scale above 1000, the number of edges in complete graph is reduced by more than 30 times.

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