Related papers: Approximating Graphic TSP by Matchings
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…
We give a polynomial time, $(1+\epsilon)$-approximation algorithm for the traveling repairman problem (TRP) in the Euclidean plane and on weighted trees. This improves on the known quasi-polynomial time approximation schemes for these…
We give approximation schemes for Subset TSP and Steiner Tree on unit disk graphs, and more generally, on intersection graphs of similarly sized connected fat (not necessarily convex) polygons in the plane. As a first step towards this…
Interactions between two entities often occur at specific timestamps, which can be modeled as a temporal graph. Exploring the relationships between vertices based on temporal paths is one of the fundamental tasks. In this paper, we conduct…
What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on…
The Trigger Arc Traveling Salesman Problem (TA-TSP) extends the classical TSP by introducing dynamic arc costs that change when specific "trigger" arcs are traversed, modeling scenarios such as warehouse operations with compactable storage…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
For NP-hard combinatorial optimization problems, it is usually difficult to find high-quality solutions in polynomial time. The design of either an exact algorithm or an approximate algorithm for these problems often requires significantly…
In this paper we investigate the integrality ratio of the standard LP relaxation for the metric $s-t$ Path TSP. We make a near-optimal choice for an auxiliary function used in the analysis of Traub and Vygen which leads to an improved upper…
In the k-edge-connected spanning subgraph problem we are given a graph (V, E) and costs for each edge, and want to find a minimum-cost subset F of E such that (V, F) is k-edge-connected. We show there is a constant eps > 0 so that for all k…
The aim of the paper is to compare different approximation algorithms for the travelling salesperson problem. We pick the most popular and widespread methods known in the literature and contrast them with a novel approach (the polygonal…
Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph…
The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to transform one graph to another. It is NP-hard to compute in general, and a…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
We apply the stabilizer formalism to the Maximum Cut problem, and obtain a new greedy construction heuristic. It turns out to be an elegant synthesis of the edge-contraction and differencing edge-contraction approaches. Utilizing the…
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In…
Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…
Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to biological and biomedical problems. The graph matching…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including…