Related papers: Parameterized TSP: Beating the Average
We propose a simple and exact method for the Traveling Salesman Problem with Time Windows and Makespan objective (\TSPTW-M) that solves all instances of the classical benchmark with $50$ or more customers in less than ten seconds each.…
In response to the Amazon Last-Mile Routing Challenge, Team Permission Denied proposes a hierarchical Travelling Salesman Problem (TSP) optimization with a customized cost matrix. The higher level TSP solves for the zone sequence while the…
The cost due to delay in services may be intrinsically different for various applications of vehicle routing such as medical emergencies, logistical operations, and ride-sharing. We study a fundamental generalization of the Traveling…
We present a fast combinatorial $3/4$-approximation algorithm for the maximum asymmetric TSP with weights zero and one. The approximation factor of this algorithm matches the currently best one given by Bl\"aser in 2004 and based on linear…
We study the variant of the Euclidean Traveling Salesman problem where instead of a set of points, we are given a set of lines as input, and the goal is to find the shortest tour that visits each line. The best known upper and lower bounds…
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated…
Schoening presents a simple randomized algorithm for (d,k)-CSP problems with running time (d(k-1)/k)^n poly(n). Here, d is the number of colors, k is the size of the constraints, and n is the number of variables. A derandomized version of…
A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalisation of the Traveling Salesman Problem (TSP) known as the centred TSP. The method shows that the problem has clear signs of a…
Deciding if a graph is a Hamilton graph, also named the Hamilton cycle problem, is important for discrete mathematics and computer science. Due to no characterization to identify Hamilton graphs effectively, there are no tractable…
A lower bound on the solution to the traveling salesman problem is provided, which is expressed in terms of eigenvalues related to the distance matrix for the problem. This bound has many interesting properties such as transforming…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
Given an $n$-vertex $m$-edge graph $G$ with non negative edge-weights, the girth of $G$ is the weight of a shortest cycle in $G$. For any graph $G$ with polynomially bounded integer weights, we present a deterministic algorithm that…
The generalized Petersen graph $G(n, k)$ is a cubic graph with vertex set $V(G(n, k)) = \{v_i\}_{0 \leq i < n} \cup \{w_i\}_{0 \leq i < n}$ and edge set $E(G(n, k)) = \{v_i v_{i+1}\}_{0 \leq i < n} \cup \{w_i w_{i+k}\}_{0 \leq i < n} \cup…
In the maximum asymmetric traveling salesman problem (Max ATSP) we are given a complete directed graph with nonnegative weights on the edges and we wish to compute a traveling salesman tour of maximum weight. In this paper we give a fast…
The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide…
We show that the two problems of computing the permanent of an $n\times n$ matrix of $\operatorname{poly}(n)$-bit integers and counting the number of Hamiltonian cycles in a directed $n$-vertex multigraph with…
Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…
This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19 matrix, M, in the following way: We obtain the remainders modulo 100 of each of the…
In his seminal 1976 paper, P\'osa showed that for all $p\geq C\log n/n$, the binomial random graph $G(n,p)$ is with high probability Hamiltonian. This leads to the following natural questions, which have been extensively studied: How well…