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We revisit a graph width parameter that we dub bipartite treewidth (btw). Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number, and is closely related to odd-minors. Intuitively, a…

Data Structures and Algorithms · Computer Science 2025-12-01 Lars Jaffke , Laure Morelle , Ignasi Sau , Dimitrios M. Thilikos

Treewidth is a parameter that emerged from the study of minor closed classes of graphs (i.e. classes closed under vertex and edge deletion, and edge contraction). It in some sense describes the global structure of a graph. Roughly, a graph…

Combinatorics · Mathematics 2022-02-02 Tara Abrishami , Maria Chudnovsky , Kristina Vušković

We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…

Data Structures and Algorithms · Computer Science 2025-12-18 Yonggang Jiang , Yaowei Long , Thatchaphol Saranurak , Benyu Wang

Structural parameters of graphs, such as treewidth, play a central role in the study of the parameterized complexity of graph problems. Motivated by the study of parametrized algorithms on phylogenetic networks, scanwidth was introduced…

Computational Complexity · Computer Science 2026-02-09 Jannik Schestag , Norbert Zeh

In the Telephone Broadcasting problem, the goal is to disseminate a message from a given source vertex of an input graph to all other vertices in the minimum number of rounds, where at each round, an informed vertex can send the message to…

Data Structures and Algorithms · Computer Science 2025-02-12 Aida Aminian , Shahin Kamali , Seyed-Mohammad Seyed-Javadi , Sumedha

In the Weighted Treewidth-$\eta$ Deletion problem we are given a node-weighted graph $G$ and we look for a vertex subset $X$ of minimum weight such that the treewidth of $G-X$ is at most $\eta$. We show that Weighted Treewidth-$\eta$…

Data Structures and Algorithms · Computer Science 2024-10-10 Michał Włodarczyk

We consider the following general network design problem on directed graphs. The input is an asymmetric metric $(V,c)$, root $r^{*}\in V$, monotone submodular function $f:2^V\rightarrow \mathbb{R}_+$ and budget $B$. The goal is to find an…

Data Structures and Algorithms · Computer Science 2019-04-03 Rohan Ghuge , Viswanath Nagarajan

The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…

Data Structures and Algorithms · Computer Science 2020-09-17 Tesshu Hanaka , Yasuaki Kobayashi , Taiga Sone

Graphs with bounded highway dimension were introduced by Abraham et al. [SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distribution over bounded treewidth graphs with arbitrarily small…

Data Structures and Algorithms · Computer Science 2019-06-20 Andreas Emil Feldmann , Wai Shing Fung , Jochen Könemann , Ian Post

We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-31 Taisuke Izumi , Naoki Kitamura , Takamasa Naruse , Gregory Schwartzman

The k-CO-PATH SET problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O^*(1.588^k) for…

Data Structures and Algorithms · Computer Science 2016-07-29 Blair D. Sullivan , Andrew van der Poel

Rank-width is a width parameter of graphs describing whether it is possible to decompose a graph into a tree-like structure by `simple' cuts. This survey aims to summarize known algorithmic and structural results on rank-width of graphs.

Combinatorics · Mathematics 2018-05-16 Sang-il Oum

The twin-width of a graph measures its distance to co-graphs and generalizes classical width concepts such as tree-width or rank-width. Since its introduction in 2020 (Bonnet et. al. 2020), a mass of new results has appeared relating twin…

Combinatorics · Mathematics 2024-11-21 Irene Heinrich , Simon Raßmann

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

Data Structures and Algorithms · Computer Science 2017-11-15 Pan Peng , Christian Sohler

We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.…

Data Structures and Algorithms · Computer Science 2015-04-29 Krishnendu Chatterjee , Rasmus Ibsen-Jensen , Andreas Pavlogiannis

Tree decompositions were developed by Robertson and Seymour. Since then algorithms have been developed to solve intractable problems efficiently for graphs of bounded treewidth. In this paper we extend tree decompositions to allow cycles to…

Data Structures and Algorithms · Computer Science 2007-05-23 Melanie J. Agnew , Christopher M. Homan

A \emph{$t$-treewidth-modulator} of a graph $G$ is a set $X \subseteq V(G)$ such that the treewidth of $G-X$ is at most some constant $t-1$. In this paper, we present a novel algorithm to compute a decomposition scheme for graphs $G$ that…

Data Structures and Algorithms · Computer Science 2012-08-02 Eun Jung Kim , Alexander Langer , Christophe Paul , Felix Reidl , Peter Rossmanith , Ignasi Sau , Somnath Sikdar

The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…

Data Structures and Algorithms · Computer Science 2024-08-19 Dror Chawin , Ishay Haviv

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…

Data Structures and Algorithms · Computer Science 2016-10-05 Thomas Bosman

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…

Data Structures and Algorithms · Computer Science 2014-05-23 Danupon Nanongkai