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We study the tractability of the maximum independent set problem from the viewpoint of graph width parameters, with the goal of defining a width parameter that is as general as possible and allows to solve independent set in polynomial-time…

Data Structures and Algorithms · Computer Science 2023-08-01 Benjamin Bergougnoux , Tuukka Korhonen , Igor Razgon

Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and…

Computational Complexity · Computer Science 2020-07-29 Hubie Chen , Georg Gottlob , Matthias Lanzinger , Reinhard Pichler

We study the parameterized complexity of the classical Edge Hamiltonian Path problem and give several fixed-parameter tractability results. First, we settle an open question of Demaine et al. by showing that Edge Hamiltonian Path is FPT…

Data Structures and Algorithms · Computer Science 2014-03-11 Michael Lampis , Kazuhisa Makino , Valia Mitsou , Yushi Uno

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…

Artificial Intelligence · Computer Science 2009-03-04 Christian Bessiere , Emmanuel Hebrard , Brahim Hnich , Zeynep Kiziltan , Toby Walsh

We consider problems in which a simple path of fixed length, in an undirected graph, is to be shifted from a start position to a goal position by moves that add an edge to either end of the path and remove an edge from the other end. We…

Data Structures and Algorithms · Computer Science 2019-05-03 Erik D. Demaine , David Eppstein , Adam Hesterberg , Kshitij Jain , Anna Lubiw , Ryuhei Uehara , Yushi Uno

We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…

Computational Complexity · Computer Science 2023-10-24 Hans L. Bodlaender , Carla Groenland , Céline M. F. Swennenhuis

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

Optimization and Control · Mathematics 2026-02-09 Alberto Del Pia

Given a graph $G$ and two independent sets of $G$, the independent set reconfiguration problem asks whether one independent set can be transformed into the other by moving a single vertex at a time, such that at each intermediate step we…

Discrete Mathematics · Computer Science 2024-02-06 Valentin Bartier , Nicolas Bousquet , Moritz Mühlenthaler

Fix a positive integer $r$, and a graph $G$ that is $K_{3,r}$-minor-free. Let $I_s$ and $I_t$ be two independent sets in $G$, each of size $k$. We begin with a ``token'' on each vertex of $I_s$ and seek to move all tokens to $I_t$, by…

Combinatorics · Mathematics 2025-06-05 Nicolas Bousquet , Daniel W. Cranston

We study the problem of deciding reconfigurability of target sets of a graph. Given a graph $G$ with vertex thresholds $\tau$, consider a dynamic process in which vertex $v$ becomes activated once at least $\tau(v)$ of its neighbors are…

Data Structures and Algorithms · Computer Science 2022-12-07 Naoto Ohsaka

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…

Numerical Analysis · Mathematics 2018-11-27 Yiqiu Dong , Carola-Bibiane Schönlieb

We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size $k$ are reconfigurable in an $n$-vertex interval graph, then there is a reconfiguration sequence of…

Combinatorics · Mathematics 2021-05-10 Marcin Briański , Stefan Felsner , Jędrzej Hodor , Piotr Micek

The problem of deciding whether a biconnected planar digraph $G=(V,E)$ can be augmented to become an $st$-planar graph by adding a set of oriented edges $E' \subseteq V \times V$ is known to be NP-complete. We show that the problem is…

Data Structures and Algorithms · Computer Science 2023-09-28 Liana Khazaliya , Philipp Kindermann , Giuseppe Liotta , Fabrizio Montecchiani , Kirill Simonov

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…

Data Structures and Algorithms · Computer Science 2018-12-31 Tatsuhiko Hatanaka , Takehiro Ito , Xiao Zhou

Traditionally, reconfiguration problems ask the question whether a given solution of an optimization problem can be transformed to a target solution in a sequence of small steps that preserve feasibility of the intermediate solutions. In…

Discrete Mathematics · Computer Science 2019-01-25 Mark de Berg , Bart M. P. Jansen , Debankur Mukherjee

We show that CSP is fixed-parameter tractable when parameterized by the treewidth of a backdoor into any tractable CSP problem over a finite constraint language. This result combines the two prominent approaches for achieving tractability…

Data Structures and Algorithms · Computer Science 2016-10-12 Robert Ganian , M. S. Ramanujan , Stefan Szeider

The propositional planning problem is a notoriously difficult computational problem. Downey et al. (1999) initiated the parameterized analysis of planning (with plan length as the parameter) and B\"ackstr\"om et al. (2012) picked up this…

Data Structures and Algorithms · Computer Science 2013-07-16 Christer Bäckström , Peter Jonsson , Sebastian Ordyniak , Stefan Szeider

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

Data Structures and Algorithms · Computer Science 2022-12-22 Kitty Meeks , Fiona Skerman

Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…

Data Structures and Algorithms · Computer Science 2018-09-05 Robert Ganian , Sebastian Ordyniak