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This paper focuses on finding a spanning tree of a graph to maximize the number of its internal vertices. We present an approximation algorithm for this problem which can achieve a performance ratio $\frac{4}{3}$ on undirected simple…

Data Structures and Algorithms · Computer Science 2014-09-15 Xingfu Li , Daming Zhu

Finding a minimum-weight strongly connected spanning subgraph of an edge-weighted directed graph is equivalent to the weighted version of the well-known strong connectivity augmentation problem. This problem is NP-hard, and a simple…

Data Structures and Algorithms · Computer Science 2024-09-19 Ryoma Norose , Yutaro Yamaguchi

The Maximum Agreement Forest (Maf) problem is a well-studied problem in evolutionary biology, which asks for a largest common subforest of a given collection of phylogenetic trees with identical leaf label-set. However, the previous work…

Data Structures and Algorithms · Computer Science 2014-11-04 Feng Shi , Jianer Chen , Qilong Feng , Xiaojun Ding , Jianxin Wang

We study tree approximations to classical two-body partition functions on sparse and loopy graphs via the Brydges-Kennedy-Abdessalam-Rivasseau forest expansion. We show that for sparse graphs (with large cycles), the partition function…

Combinatorics · Mathematics 2024-02-08 Francesco Caravelli

In the Tree Augmentation problem we are given a tree $T=(V,F)$ and a set $E \subseteq V \times V$ of edges with positive integer costs $\{c_e:e \in E\}$. The goal is to augment $T$ by a minimum cost edge set $J \subseteq E$ such that $T…

Data Structures and Algorithms · Computer Science 2018-12-27 Zeev Nutov

Given an edge-weighted metric complete graph with $n$ vertices, the maximum weight metric triangle packing problem is to find a set of $n/3$ vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several…

Data Structures and Algorithms · Computer Science 2024-02-14 Jingyang Zhao , Mingyu Xiao

We present efficient algorithms for computing a maximum agreement forest (MAF) of a pair of multifurcating (nonbinary) rooted trees. Our algorithms match the running times of the currently best algorithms for the binary case. The size of an…

Data Structures and Algorithms · Computer Science 2013-05-03 Chris Whidden , Robert G. Beiko , Norbert Zeh

Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…

Computational Geometry · Computer Science 2020-10-23 Stav Ashur , Matthew J. Katz

The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…

Data Structures and Algorithms · Computer Science 2021-01-18 Alexander van der Grinten , Eugenio Angriman , Maria Predari , Henning Meyerhenke

The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…

Data Structures and Algorithms · Computer Science 2022-03-01 Eiichiro Sato

We study the prize-collecting version of the Node-weighted Steiner Tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for planar NWPCST. We then show…

Data Structures and Algorithms · Computer Science 2016-01-12 Jarosław Byrka , Mateusz Lewandowski , Carsten Moldenhauer

We design a 3/2 approximation algorithm for the Generalized Steiner Tree problem (GST) in metrics with distances 1 and 2. This is the first polynomial time approximation algorithm for a wide class of non-geometric metric GST instances with…

Computational Complexity · Computer Science 2008-12-12 Piotr Berman , Marek Karpinski , Alex Zelikovsky

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…

Discrete Mathematics · Computer Science 2012-09-18 András Sebő , Jens Vygen

We obtain a polynomial-time 17/12-approximation algorithm for the minimum-cost 2-vertex-connected spanning subgraph problem, restricted to graphs of minimum degree at least 3. Our algorithm uses the framework of ear-decompositions for…

Data Structures and Algorithms · Computer Science 2017-01-18 Vishnu V. Narayan

Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…

Data Structures and Algorithms · Computer Science 2019-11-26 Tobias Mömke , Andreas Wiese

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…

Data Structures and Algorithms · Computer Science 2023-07-10 Elena Grigorescu , Nithish Kumar , Young-San Lin

We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…

Data Structures and Algorithms · Computer Science 2019-02-25 Samuel Fiorini , Gwenaël Joret , Oliver Schaudt

In this paper we reassess the parameterized complexity and approximability of the well-studied Steiner Forest problem in several graph classes of bounded width. The problem takes an edge-weighted graph and pairs of vertices as input, and…

Data Structures and Algorithms · Computer Science 2024-07-26 Andreas Emil Feldmann , Michael Lampis

We present approximation algorithms for the following NP-hard optimization problems related to bottleneck spanning trees in metric spaces. 1. The disjoint bottleneck spanning tree problem: Given $n$ pairs of points in a metric space, find…

Computational Geometry · Computer Science 2021-11-11 Ahmad Biniaz , Anil Maheshwari , Michiel Smid

The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a spanning subgraph $S$ of $G$ with the…

Data Structures and Algorithms · Computer Science 2025-07-02 Miguel Bosch-Calvo , Fabrizio Grandoni , Afrouz Jabal Ameli