Related papers: Approximating Graphic Multi-Path TSP and Graphic O…
The paper provides a description of the two recent approximation algorithms for the Asymmetric Traveling Salesman Problem, giving the intuitive description of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves the…
This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once…
We consider the Stackelberg shortest-path pricing problem, which is defined as follows. Given a graph G with fixed-cost and pricable edges and two distinct vertices s and t, we may assign prices to the pricable edges. Based on the…
We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower…
We prove the approximation ratio 8/5 for the metric $\{s,t\}$-path-TSP problem, and more generally for shortest connected $T$-joins. The algorithm that achieves this ratio is the simple "Best of Many" version of Christofides' algorithm…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
The 1-median problem (1MP) on undirected weighted graphs seeks to find a facility location minimizing the total weighted distance to all customer nodes. Although the 1MP can be solved exactly by computing the single-source shortest paths…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
The travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for…
The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…
We introduce a risk-aware multi-objective Traveling Salesperson Problem (TSP) variant, where the robot tour cost and tour reward have to be optimized simultaneously. The robot obtains reward along the edges in the graph. We study the case…
Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of the…
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…
We present a framework for efficiently solving Approximate Traveling Salesman Problem (Approximate TSP) for Quantum Computing Models. Existing representations of TSP introduce extra states which do not correspond to any permutation. We…
In Asymmetric A Priori TSP (with independent activation probabilities) we are given an instance of the Asymmetric Traveling Salesman Problem together with an activation probability for each vertex. The task is to compute a tour that…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
In this paper, an iterative algorithm is designed to compute the sparse graphs for traveling salesman problem (TSP) according to the frequency quadrilaterals so that the computation time of the algorithms for TSP will be lowered. At each…
We combine the well known Shortest Paths (SP) problem and the Bottleneck Paths (BP) problem to introduce a new problem called the Shortest Paths for All Flows (SP-AF) problem that has relevance in real life applications. We first solve the…
We show that there is a polynomial-time algorithm with approximation guarantee $\frac{3}{2}+\epsilon$ for the $s$-$t$-path TSP, for any fixed $\epsilon>0$. It is well known that Wolsey's analysis of Christofides' algorithm also works for…
This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…