Related papers: An Improved Integrality Gap for Asymmetric TSP Pat…
The Graphical Traveling Salesman Problem with release dates (GTSP-rd) is a variation of the TSP-rd where each vertex in a weighted graph $G$ must be visited at least once, respecting the release date restriction. The edges may be traversed…
We study a new version of the Traveling Salesperson Problem, called \VectorTSP, where the traveler is subject to discrete acceleration constraints, as defined in the paper-and-pencil game Racetrack (also known as Vector Racer). In this…
The paper revisits the robust $s$-$t$ path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with $n$ vertices and $k$ distinct cost functions (scenarios) defined over edges,…
We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell…
We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…
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 the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…
In this work, the relationship between a spin-glass three-dimensional (3D) Ising model with the lattice size N = mnl and the traveling salesman problem (TSP) in a 3D lattice is studied. In particular, the mathematical structures of the two…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
In this paper, we consider differential approximability of the traveling salesman problem (TSP). We show that TSP is $3/4$-differential approximable, which improves the currently best known bound $3/4 -O(1/n)$ due to Escoffier and Monnot in…
In this paper, we study the prize-collecting rural postman problem (PCRPP), a variant of the rural postman problem. Given a PCRPP instance consisting of an undirected graph whose edges have nonnegative lengths and nonnegative profits,…
We give the first constant-factor approximation for the Directed Latency problem in quasi-polynomial time. Here, the goal is to visit all nodes in an asymmetric metric with a single vehicle starting at a depot $r$ to minimize the average…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
We improve the approximation ratio for the Asymmetric TSP to less than 15. We also obtain improved ratios for the special case of unweighted digraphs and the generalization where we ask for a minimum-cost tour with given (distinct)…
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…
We present a $1.5$-approximation for the Metric Path Traveling Salesman Problem (Path TSP). All recent improvements on Path TSP crucially exploit a structural property shown by An, Kleinberg, and Shmoys [Journal of the ACM, 2015], namely…
The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour of $n$ cities that visits each city $c$ a prescribed number $k_c$ of times. Travel costs may be asymmetric, and visiting a city twice in a row may incur a…
We present an exact formulation of the symmetric Traveling Salesman Problem (TSP) that replaces the classical edge-selection view with a surface-building approach. Instead of selecting edges to form a cycle, the model selects a set of…
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…
The Traveling Salesman Problem (TSP) is a classic and extensively studied problem with numerous real-world applications in artificial intelligence and operations research. It is well-known that TSP admits a constant approximation ratio on…