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We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-08 Chetan Gupta , Rustam Latypov , Yannic Maus , Shreyas Pai , Simo Särkkä , Jan Studený , Jukka Suomela , Jara Uitto , Hossein Vahidi

We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…

Data Structures and Algorithms · Computer Science 2015-11-05 Fedor V. Fomin , Daniel Lokshtanov , Michał Pilipczuk , Saket Saurabh , Marcin Wrochna

For a given graph $G=(V,\, E)$ with a terminal set $S$ and a selected root $r\in S$, a positive integer cost and a delay on every edge and a delay constraint $D\in Z^{+}$, the shallow-light Steiner tree (\emph{SLST}) problem is to compute a…

Data Structures and Algorithms · Computer Science 2013-09-04 Longkun Guo , Kewen Liao

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

We present a parameterized dichotomy for the \textsc{$k$-Sparsest Cut} problem in weighted and unweighted versions. In particular, we show that the weighted \textsc{$k$-Sparsest Cut} problem is NP-hard for every $k\geq 3$ even on graphs…

Computational Complexity · Computer Science 2023-04-04 Ramin Javadi , Amir Nikabadi

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…

Data Structures and Algorithms · Computer Science 2015-06-30 Danny Hermelin , Moshe Kaspi , Christian Komusiewicz , Barak Navon

Shifted combinatorial optimization is a new nonlinear optimization framework which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. This framework captures well…

Computational Complexity · Computer Science 2021-02-25 Jakub Gajarský , Petr Hliněný , Martin Koutecký , Shmuel Onn

Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples…

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two…

Logic in Computer Science · Computer Science 2017-02-10 Johannes Fichte , Markus Hecher , Michael Morak , Stefan Woltran

Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…

Data Structures and Algorithms · Computer Science 2019-02-21 Max Bannach , Malte Skambath , Till Tantau

The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this…

Data Structures and Algorithms · Computer Science 2023-11-21 Johannes Rauch , Dieter Rautenbach , Uéverton S. Souza

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

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…

Computational Complexity · Computer Science 2022-12-20 Falko Hegerfeld , Stefan Kratsch

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

A Fixed-Parameter Tractable (\FPT) $\rho$-approximation algorithm for a minimization (resp. maximization) parameterized problem $P$ is an FPT algorithm that, given an instance $(x, k)\in P$ computes a solution of cost at most $k \cdot…

Data Structures and Algorithms · Computer Science 2013-08-19 Rajesh Chitnis , MohammadTaghi Hajiaghayi , Guy Kortsarz

The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…

Computational Complexity · Computer Science 2018-10-11 Katrin Casel , Henning Fernau , Mehdi Khosravian Ghadikolaei , Jérôme Monnot , Florian Sikora

We introduce a new technique for designing fixed-parameter algorithms for cut problems, namely randomized contractions. We apply our framework to obtain the first FPT algorithm for the Unique Label Cover problem and new FPT algorithms with…

Data Structures and Algorithms · Computer Science 2016-07-20 Rajesh Chitnis , Marek Cygan , MohammadTaghi Hajiaghayi , Marcin Pilipczuk , Michał Pilipczuk

Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional…

Data Structures and Algorithms · Computer Science 2019-11-22 Rajesh Chitnis , Graham Cormode

We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-31 Taisuke Izumi , Naoki Kitamura , Takamasa Naruse , Gregory Schwartzman

Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time $f(k)n^{O(1)}$ and space $f(k)\log(n)$ (for some computable function f). We give a wide variety of…

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