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In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…

Data Structures and Algorithms · Computer Science 2020-09-15 Daniel Lokshtanov , Saket Saurabh , Vaishali Surianarayanan

There is substantial literature dealing with fixed parameter algorithms for the dominating set problem on various families of graphs. In this paper, we give a $k^{O(dk)} n$ time algorithm for finding a dominating set of size at most $k$ in…

Data Structures and Algorithms · Computer Science 2008-12-18 Noga Alon , Shai Gutner

The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…

Data Structures and Algorithms · Computer Science 2023-06-28 Barış Can Esmer , Ariel Kulik , Dániel Marx , Daniel Neuen , Roohani Sharma

We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change…

Data Structures and Algorithms · Computer Science 2012-03-14 Daniel Lokshtanov , N. S. Narayanaswamy , Venkatesh Raman , M. S. Ramanujan , Saket Saurabh

In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length…

Data Structures and Algorithms · Computer Science 2014-02-17 Ivan Bliznets , Fedor V. Fomin , Marcin Pilipczuk , Michał Pilipczuk

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Computational Complexity · Computer Science 2021-01-06 Archontia C. Giannopoulou , George B. Mertzios , Rolf Niedermeier

The starting point of our work is a decade-old open question concerning the subexponential parameterized complexity of \textsc{2-Layer Crossing Minimization}. In this problem, the input is an $n$-vertex graph $G$ whose vertices are…

Data Structures and Algorithms · Computer Science 2025-10-16 Fedor V. Fomin , Petr A. Golovach , Tanmay Inamdar , Saket Saurabh , Meirav Zehavi

A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…

Computational Complexity · Computer Science 2026-05-05 Christian Komusiewicz , Nils Morawietz , Frank Sommer , Luca Pascal Staus

One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…

Data Structures and Algorithms · Computer Science 2018-07-16 Kyriakos Axiotis , Christos Tzamos

The Workflow Satisfiability Problem (WSP) asks whether there exists an assignment of authorized users to the steps in a workflow specification, subject to certain constraints on the assignment. The problem is NP-hard even when restricted to…

Data Structures and Algorithms · Computer Science 2015-08-28 Gregory Gutin , Magnus Wahlstrom

Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in…

Computational Complexity · Computer Science 2022-10-03 Leif Eriksson , Victor Lagerkvist

In this paper we introduce randomized branching as a tool for parameterized approximation and develop the mathematical machinery for its analysis. Our algorithms improve the best known running times of parameterized approximation algorithms…

Data Structures and Algorithms · Computer Science 2025-06-10 Ariel Kulik , Hadas Shachnai

We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…

Data Structures and Algorithms · Computer Science 2015-12-08 Fedor V. Fomin , Serge Gaspers , Daniel Lokshtanov , Saket Saurabh

Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…

Computational Complexity · Computer Science 2012-11-29 Bruno Escoffier , EunJung Kim , Vangelis Th. Paschos

In the (binary) Distinct Vectors problem we are given a binary matrix A with pairwise different rows and want to select at most k columns such that, restricting the matrix to these columns, all rows are still pairwise different. A result by…

Computational Complexity · Computer Science 2023-06-22 Marcin Pilipczuk , Manuel Sorge

We provide a general framework to exclude parameterized running times of the form $O(\ell^\beta+ n^\gamma)$ for problems that have polynomial running time lower bounds under hypotheses from fine-grained complexity. Our framework is based on…

Data Structures and Algorithms · Computer Science 2023-01-09 Klaus Heeger , André Nichterlein , Rolf Niedermeier

In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…

Data Structures and Algorithms · Computer Science 2013-07-19 Yoichi Iwata , Keigo Oka , Yuichi Yoshida

Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of…

Neural and Evolutionary Computing · Computer Science 2012-10-10 Andrew M. Sutton , Frank Neumann

The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…

Machine Learning · Computer Science 2022-05-11 Todd Wareham

For a family of graphs $\mathcal{G}$, the $\mathcal{G}$-\textsc{Contraction} problem takes as an input a graph $G$ and an integer $k$, and the goal is to decide if there exists $F \subseteq E(G)$ of size at most $k$ such that $G/F$ belongs…

Discrete Mathematics · Computer Science 2020-08-19 Saket Saurabh , Uéverton dos Santos Souza , Prafullkumar Tale