Related papers: New Approximation Algorithms for Maximum Asymmetri…
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…
In the Traveling Salesperson Problem (TSP) we are given a list of locations and the distances between each pair of them. The goal is to find the shortest possible tour that visits each location exactly once and returns to the starting…
Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…
Let $P$ be a set of points in $\mathbb{R}^d$, and let $\alpha \ge 1$ be a real number. We define the distance between two points $p,q\in P$ as $|pq|^{\alpha}$, where $|pq|$ denotes the standard Euclidean distance between $p$ and $q$. We…
We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant…
Prize-Collecting TSP is a variant of the traveling salesperson problem where one may drop vertices from the tour at the cost of vertex-dependent penalties. The quality of a solution is then measured by adding the length of the tour and the…
This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual,…
Motivated by the well known four-thirds conjecture for the traveling salesman problem (TSP), we study the problem of {\em uniform covers}. A graph $G=(V,E)$ has an $\alpha$-uniform cover for TSP (2EC, respectively) if the everywhere…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
We provide exact and approximation methods for solving a geometric relaxation of the Traveling Salesman Problem (TSP) that occurs in curve reconstruction: for a given set of vertices in the plane, the problem Minimum Perimeter Polygon (MPP)…
In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate…
In this paper we study the classical no-wait flowshop scheduling problem with makespan objective (F|no-wait|C_max in the standard three-field notation). This problem is well-known to be a special case of the asymmetric traveling salesman…
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…
This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in…
The Asymmetric Traveling Salesperson Path Problem (ATSPP) is one where, given an asymmetric metric space $(V,d)$ with specified vertices s and t, the goal is to find an s-t path of minimum length that passes through all the vertices in V.…
In this paper, we provide a novel strategy for solving Traveling Salesman Problem, which is a famous combinatorial optimization problem studied intensely in the TCS community. In particular, we consider the imitation learning framework,…
We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the…
We develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification…
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…
The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…