Related papers: Improving polynomial bounds for the Graphical Trav…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
The Directed Traveling Salesman Problem (DTSP) is a variant of the classical Traveling Salesman Problem in which the edges in the graph are directed and a vertex and edge can be visited multiple times. The goal is to find a directed closed…
Solutions to the Traveling Salesperson Problem (TSP) have practical applications to processes in transportation, logistics, and automation, yet must be computed with minimal delay to satisfy the real-time nature of the underlying tasks.…
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says…
The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits…
We study integrality gaps and approximability of two closely related problems on directed graphs. Given a set V of n nodes in an underlying asymmetric metric and two specified nodes s and t, both problems ask to find an s-t path visiting…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding…
The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and…
We provide a new upper bound for traveling salesman problem (TSP) in cubic graphs, i.e. graphs with maximum vertex degree three, and prove that the problem for an $n$-vertex graph can be solved in $O(1.2553^n)$ time and in linear space. We…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…
We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related {\em maximum path cover} problem, which asks for a collection of vertex disjoint paths that include the maximum number of…
In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…
The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits each vertex in an undirected edge-weighted and not necessarily complete graph. We present a problem kernel with…
The traveling salesman problem (TSP) is one of the most prominent combinatorial optimization problems. Given a complete graph G = (V, E) and non-negative distances d for every edge, the TSP asks for a shortest tour through all vertices with…
The generalized multiple depot traveling salesmen problem (GMDTSP) is a variant of the multiple depot traveling salesmen problem (MDTSP), where each salesman starts at a distinct depot, the targets are partitioned into clusters and at least…
An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…
Given a traveling salesman problem (TSP) tour $H$ in graph $G$ a $k$-move is an operation which removes $k$ edges from $H$, and adds $k$ edges of $G$ so that a new tour $H'$ is formed. The popular $k$-OPT heuristics for TSP finds a local…
The Traveling Salesman Problem (TSP) in the $d$-dimensional Euclidean space is among the oldest and most famous NP-hard optimization problems. In breakthrough works, Arora [J. ACM 1998] and Mitchell [SICOMP 1999] gave the first polynomial…