English
Related papers

Related papers: Faster algorithm for Unique $(k,2)$-CSP

200 papers

For many constraint satisfaction problems, the algorithm which chooses a random assignment achieves the best possible approximation ratio. For instance, a simple random assignment for {\sc Max-E3-Sat} allows 7/8-approximation and for every…

Data Structures and Algorithms · Computer Science 2011-10-17 Eun Jung Kim , Ryan Williams

We consider the question of approximating Max 2-CSP where each variable appears in at most $d$ constraints (but with possibly arbitrarily large alphabet). There is a simple $(\frac{d+1}{2})$-approximation algorithm for the problem. We prove…

Data Structures and Algorithms · Computer Science 2023-09-11 Euiwoong Lee , Pasin Manurangsi

We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…

Discrete Mathematics · Computer Science 2010-01-14 Alexander D. Scott , Gregory B. Sorkin

In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…

Computational Complexity · Computer Science 2007-05-23 Peter Jonsson , Mikael Klasson , Andrei Krokhin

This paper studies complete $k$-Constraint Satisfaction Problems (CSPs), where an $n$-variable instance has exactly one nontrivial constraint for each subset of $k$ variables, i.e., it has $\binom{n}{k}$ constraints. A recent work started a…

Data Structures and Algorithms · Computer Science 2025-04-29 Aditya Anand , Euiwoong Lee , Davide Mazzali , Amatya Sharma

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

We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…

Computational Complexity · Computer Science 2021-07-14 Albert Atserias , Víctor Dalmau

The \emph{Workflow Satisfiability Problem (WSP)} is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether…

Data Structures and Algorithms · Computer Science 2015-05-18 David Cohen , Jason Crampton , Andrei Gagarin , Gregory Gutin , Mark Jones

PPSZ is the fastest known algorithm for (d,k)-CSP problems, for most values of d and k. It goes through the variables in random order and sets each variable randomly to one of the d colors, excluding those colors that can be ruled out by…

Data Structures and Algorithms · Computer Science 2021-09-08 Shibo Li , Dominik Scheder

We show that several important resource allocation problems in wireless networks fit within the common framework of Constraint Satisfaction Problems (CSPs). Inspired by the requirements of these applications, where variables are located at…

Artificial Intelligence · Computer Science 2013-09-19 K. R. Duffy , C. Bordenave , D. J. Leith

The family of $(k,\ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic problem is to decide whether a given…

Data Structures and Algorithms · Computer Science 2026-04-15 Bence Deák , Péter Madarasi

Raghavendra (STOC 2008) gave an elegant and surprising result: if Khot's Unique Games Conjecture (STOC 2002) is true, then for every constraint satisfaction problem (CSP), the best approximation ratio is attained by a certain simple…

Data Structures and Algorithms · Computer Science 2010-11-01 Yuichi Yoshida

For the constrained 2-means problem, we present a $O\left(dn+d({1\over\epsilon})^{O({1\over \epsilon})}\log n\right)$ time algorithm. It generates a collection $U$ of approximate center pairs $(c_1, c_2)$ such that one of pairs in $U$ can…

Computational Geometry · Computer Science 2018-08-14 Qilong Feng , Bin Fu

The exponential-time hypothesis (ETH) states that 3-SAT is not solvable in subexponential time, i.e. not solvable in O(c^n) time for arbitrary c > 1, where n denotes the number of variables. Problems like k-SAT can be viewed as special…

Computational Complexity · Computer Science 2017-06-20 Peter Jonsson , Victor Lagerkvist , Biman Roy

Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…

Data Structures and Algorithms · Computer Science 2014-07-30 Amey Bhangale , Swastik Kopparty , Sushant Sachdeva

We show that the CNF satisfiability problem (SAT) can be solved in time $O^*(1.1199^{(d-2)n})$, where $d$ is either the maximum number of occurrences of any variable or the average number of occurrences of all variables if no variable…

Data Structures and Algorithms · Computer Science 2024-11-13 Sanjay Jain , Tzeh Yuan Neoh , Frank Stephan

A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…

Logic in Computer Science · Computer Science 2022-04-01 Michael Pinsker

Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause…

Data Structures and Algorithms · Computer Science 2008-01-22 Liang Li , Xin Li , Tian Liu , Ke Xu

The estimation of phase transitions in random boolean Constraint Satisfaction Problems (CSP) is based on two fundamental tools: the first and second moment methods. While the first moment method on the number of solutions permits to compute…

Discrete Mathematics · Computer Science 2011-09-27 Yacine Boufkhad , Olivier Dubois

In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in undirected graphs. For unweighted graphs, we provide an algorithm for $2$-approximate APSP in $\tilde O(n^{2.5-r}+n^{\omega(r)})$ time, for any…

Data Structures and Algorithms · Computer Science 2023-10-31 Michal Dory , Sebastian Forster , Yael Kirkpatrick , Yasamin Nazari , Virginia Vassilevska Williams , Tijn de Vos