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We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…

Data Structures and Algorithms · Computer Science 2024-08-27 Friedrich Eisenbrand , Lars Rohwedder , Karol Węgrzycki

The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16). Simply put, the main goal is to design streaming algorithms for parameterized problems…

Computational Complexity · Computer Science 2019-10-03 Arijit Bishnu , Arijit Ghosh , Sudeshna Kolay , Gopinath Mishra , Saket Saurabh

In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…

Optimization and Control · Mathematics 2022-11-30 D. V. Gribanov , D. S. Malyshev , P. M. Pardalos , S. I. Veselov

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems; however, also structural parameters have been…

Data Structures and Algorithms · Computer Science 2015-07-21 Eduard Eiben , Robert Ganian , Stefan Szeider

Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…

Data Structures and Algorithms · Computer Science 2021-02-12 Ajinkya Gaikwad , Soumen Maity

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Data Structures and Algorithms · Computer Science 2013-09-25 Vincent Blondel , Kyomin Jung , Pushmeet Kohli , Devavrat Shah

The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive…

Computational Complexity · Computer Science 2019-05-10 Eva-Maria C. Hols , Stefan Kratsch , Astrid Pieterse

In this paper, we introduce the concept of Density-Balanced Subset in a matroid, in which independent sets can be sampled so as to guarantee that (i) each element has the same probability to be sampled, and (ii) those events are negatively…

Data Structures and Algorithms · Computer Science 2023-08-15 François Sellier

This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…

Combinatorics · Mathematics 2023-01-24 Péter Madarasi

In the Topological Minor Deletion (TM-Deletion) problem input consists of an undirected graph $G$, a family of undirected graphs ${\cal F}$ and an integer $k$. The task is to determine whether $G$ contains a set of vertices $S$ of size at…

Data Structures and Algorithms · Computer Science 2020-01-08 Fedor V. Fomin , Daniel Lokshtanov , Fahad Panolan , Saket Saurabh , Meirav Zehavi

The elimination distance to some target graph property P is a general graph modification parameter introduced by Bulian and Dawar. We initiate the study of elimination distances to graph properties expressible in first-order logic. We…

Logic in Computer Science · Computer Science 2021-04-08 Fedor V. Fomin , Petr A. Golovach , Dimitrios M. Thilikos

In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal $st$-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In…

Computational Complexity · Computer Science 2025-02-18 Ajinkya Gaikwad , Hitendra Kumar , Soumen Maity , Saket Saurabh , Roohani Sharma

We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…

Data Structures and Algorithms · Computer Science 2014-01-07 Alexandr Andoni , Aleksandar Nikolov , Krzysztof Onak , Grigory Yaroslavtsev

The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…

Data Structures and Algorithms · Computer Science 2017-11-29 Bireswar Das , Murali Krishna Enduri , Neeldhara Misra , I. Vinod Reddy

The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-04-18 Saeed Akhoondian Amiri , Stefan Schmid , Sebastian Siebertz

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by…

Data Structures and Algorithms · Computer Science 2023-11-09 Sylvain Guillemot

A set $S$ of vertices of a graph is a defensive alliance if, for each element of $S$, the majority of its neighbours is in $S$. We consider the notion of local minimality in this paper. We are interested in locally minimal defensive…

Computational Complexity · Computer Science 2023-03-06 Ajinkya Gaikwad , Soumen Maity , Shuvam Kant Tripathi

In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an…

Optimization and Control · Mathematics 2021-12-14 Stephan Helfrich , Arne Herzel , Stefan Ruzika , Clemens Thielen

The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and…

Data Structures and Algorithms · Computer Science 2016-02-09 Rémy Belmonte , Fedor V. Fomin , Petr A. Golovach , M. S. Ramanujan

A set $D$ of vertices of a graph is a \emph{defensive alliance} if, for each element of $D$, the majority of its neighbours are in $D$. We consider the notion of local minimality in this paper. We are interested in finding a locally minimal…

Data Structures and Algorithms · Computer Science 2023-03-05 Ajinkya Gaikwad , Soumen Maity , Saket Saurabh