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The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed…

Data Structures and Algorithms · Computer Science 2022-03-09 Hassene Aissi , Solal Attias , Da Qi Chen , R. Ravi

The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…

Data Structures and Algorithms · Computer Science 2013-09-05 Sylvain Guillemot , Dániel Marx

The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…

Discrete Mathematics · Computer Science 2017-12-18 Diane Castonguay , Elisângela Silva Dias , Leslie Richard Foulds

We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations. Existing FPT algorithms for these problems…

Data Structures and Algorithms · Computer Science 2022-07-19 Bart M. P. Jansen , Jari J. H. de Kroon , Michał Włodarczyk

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting…

Data Structures and Algorithms · Computer Science 2015-07-27 Bart M. P. Jansen

The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the…

Data Structures and Algorithms · Computer Science 2024-07-08 Svein Høgemo

We study the {\em Budgeted Dominating Set} (BDS) problem on uncertain graphs, namely, graphs with a probability distribution $p$ associated with the edges, such that an edge $e$ exists in the graph with probability $p(e)$. The input to the…

Data Structures and Algorithms · Computer Science 2021-07-08 Keerti Choudhary , Avi Cohen , N. S. Narayanaswamy , David Peleg , R. Vijayaragunathan

In the matching interdiction problem, we are given an undirected graph with weights and interdiction costs on the edges and seek to remove a subset of the edges constrained to some budget, such that the weight of a maximum weight matching…

Discrete Mathematics · Computer Science 2008-04-23 Rico Zenklusen

We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…

Data Structures and Algorithms · Computer Science 2025-07-22 Ruoxu Cen , Henry Fleischmann , George Z. Li , Jason Li , Debmalya Panigrahi

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

We consider a weighted counting problem on matchings, denoted $\textrm{PrMatching}(\mathcal{G})$, on an arbitrary fixed graph family $\mathcal{G}$. The input consists of a graph $G\in \mathcal{G}$ and of rational probabilities of existence…

Computational Complexity · Computer Science 2023-01-10 Antoine Amarilli , Mikaël Monet

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

Data Structures and Algorithms · Computer Science 2023-10-10 Siddharth Gupta , Guy Sa'ar , Meirav Zehavi

Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The…

The Metric Embedding problem takes as input two metric spaces $(X,D_X)$ and $(Y,D_Y)$, and a positive integer $d$. The objective is to determine whether there is an embedding $F:X \rightarrow Y$ such that $d_{F} \leq d$, where $d_{F}$…

Computational Geometry · Computer Science 2018-06-27 Arijit Ghosh , Sudeshna Kolay , Gopinath Mishra

One way to define the Matching Cut problem is: Given a graph $G$, is there an edge-cut $M$ of $G$ such that $M$ is an independent set in the line graph of $G$? We propose the more general Conflict-Free Cut problem: Together with the graph…

Data Structures and Algorithms · Computer Science 2023-11-03 Johannes Rauch , Dieter Rautenbach , Uéverton S. Souza

The max-k-cut problem is to partition the vertices of a weighted graph $G = (V,E)$ into $k\geq2$ disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut…

Discrete Mathematics · Computer Science 2015-11-02 Fuda Ma , Jin-Kao Hao

The weighted $\mathcal{T}$-free $2$-matching problem is the following problem: given an undirected graph $G$, a weight function on its edge set, and a set $\mathcal{T}$ of triangles in $G$, find a maximum weight $2$-matching containing no…

Data Structures and Algorithms · Computer Science 2019-11-18 Yusuke Kobayashi

We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman Problem parameterized by the…

Data Structures and Algorithms · Computer Science 2022-06-09 Bin Sheng , Gregory Gutin

In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut…

Data Structures and Algorithms · Computer Science 2021-11-12 Vincent Cohen-Addad , Tobias Mömke , Victor Verdugo

Let $G$ be a connected planar (but not yet embedded) graph and $F$ a set of additional edges not yet in $G$. The {multiple edge insertion} problem (MEI) asks for a drawing of $G+F$ with the minimum number of pairwise edge crossings, such…

Data Structures and Algorithms · Computer Science 2015-09-29 Markus Chimani , Petr Hliněný