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Given a graph $G$, a set $T$ of terminal vertices, and a demand graph $H$ on $T$, the \textsc{Multicut} problem asks for a set of edges of minimum weight that separates the pairs of terminals specified by the edges of $H$. The…

Computational Complexity · Computer Science 2026-01-27 Florian Hörsch , Dániel Marx

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Data Structures and Algorithms · Computer Science 2023-12-14 Roldan Pozo

In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…

Data Structures and Algorithms · Computer Science 2020-08-20 Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

Parameterized local search combines classic local search heuristics with the paradigm of parameterized algorithmics. While most local search algorithms aim to improve given solutions by performing one single operation on a given solution,…

Data Structures and Algorithms · Computer Science 2026-05-06 Niels Grüttemeier , Nils Morawietz , Frank Sommer

We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…

Data Structures and Algorithms · Computer Science 2008-04-21 Michael Fellows , Fedor Fomin , Daniel Lokshtanov , Elena Losievskaja , Frances A. Rosamond , Saket Saurabh

We study {\sc Cluster Edge Modification} problems with constraints on the size of the clusters. A graph $G$ is a cluster graph if every connected component of $G$ is a clique. In a typical {\sc Cluster Edge Modification} problem such as the…

Data Structures and Algorithms · Computer Science 2024-09-05 Jayakrishnan Madathil , Kitty Meeks

The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…

Data Structures and Algorithms · Computer Science 2019-06-27 Fabrizio Grandoni , Stefan Kratsch , Andreas Wiese

We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…

Combinatorics · Mathematics 2016-09-06 Madhav V. Marathe , Harry B. Hunt , S. S. Ravi

The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…

Data Structures and Algorithms · Computer Science 2022-04-12 Adil Erzin , Roman Plotnikov , Ilya Ladygin

Many well-known NP-hard algorithmic problems on directed graphs resist efficient parametrisations with most known width measures for directed graphs, such as directed treewidth, DAG-width, Kelly-width and many others. While these focus on…

Discrete Mathematics · Computer Science 2019-05-31 Raphael Steiner , Sebastian Wiederrecht

We present a new approximation algorithm for the treewidth problem which finds an upper bound on the treewidth and constructs a corresponding tree decomposition as well. Our algorithm is a faster variation of Reed's classical algorithm. For…

Data Structures and Algorithms · Computer Science 2022-06-24 Mahdi Belbasi , Martin Fürer

Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but…

Data Structures and Algorithms · Computer Science 2023-11-15 Zhengren Wang , Yi Zhou , Chunyu Luo , Mingyu Xiao , Jin-Kao Hao

We study the problem of optimal traffic prediction and monitoring in large-scale networks. Our goal is to determine which subset of K links to monitor in order to "best" predict the traffic on the remaining links in the network. We consider…

Data Structures and Algorithms · Computer Science 2013-12-04 Michael Kallitsis , Stilian Stoev , George Michailidis

A graph is called a $(k,\rho)$-graph iff every node can reach $\rho$ of its nearest neighbors in at most k hops. This property proved useful in the analysis and design of parallel shortest-path algorithms. Any graph can be transformed into…

Data Structures and Algorithms · Computer Science 2024-02-13 Alexander Leonhardt , Ulrich Meyer , Manuel Penschuck

$ $We study the $d$-Uniform Hypergraph Matching ($d$-UHM) problem: given an $n$-vertex hypergraph $G$ where every hyperedge is of size $d$, find a maximum cardinality set of disjoint hyperedges. For $d\geq3$, the problem of finding the…

Data Structures and Algorithms · Computer Science 2020-09-22 Oussama Hanguir , Clifford Stein

We consider the weighted $k$-set packing problem, in which we are given a collection of weighted sets, each with at most $k$ elements and must return a collection of pairwise disjoint sets with maximum total weight. For $k = 3$, this…

Data Structures and Algorithms · Computer Science 2023-01-19 Theophile Thiery , Justin Ward

In the minimum Multicut problem, the input is an edge-weighted supply graph $G=(V,E)$ and a simple demand graph $H=(V,F)$. Either $G$ and $H$ are directed (DMulC) or both are undirected (UMulC). The goal is to remove a minimum weight set of…

Discrete Mathematics · Computer Science 2016-08-01 Chandra Chekuri , Vivek Madan

Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…

Data Structures and Algorithms · Computer Science 2017-09-11 Petr Kolman

In a network consisting of n nodes, our goal is to identify the most central k nodes with respect to the proposed definitions of centrality. Depending on the specific application, there exist several metrics for quantifying k-centrality,…

Combinatorics · Mathematics 2024-06-11 Karim Shahbaz , Madhu N. Belur , Chayan Bhawal , Debasattam Pal

Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \times B$ so that any point of $A \cup B$ appears in…

Data Structures and Algorithms · Computer Science 2019-03-25 Pankaj K. Agarwal , Hsien-Chih Chang , Allen Xiao