English
Related papers

Related papers: Global Cardinality Constraints Make Approximating …

200 papers

A constraint satisfaction problem (CSP), $\textsf{Max-CSP}(\mathcal{F})$, is specified by a finite set of constraints $\mathcal{F} \subseteq \{[q]^k \to \{0,1\}\}$ for positive integers $q$ and $k$. An instance of the problem on $n$…

Computational Complexity · Computer Science 2024-02-27 Chi-Ning Chou , Alexander Golovnev , Madhu Sudan , Santhoshini Velusamy

We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…

Computational Complexity · Computer Science 2026-05-15 Dor Minzer , Kai Zhe Zheng

In the max-min allocation problem a set $P$ of players are to be allocated disjoint subsets of a set $R$ of indivisible resources, such that the minimum utility among all players is maximized. We study the restricted variant, also known as…

Data Structures and Algorithms · Computer Science 2025-01-28 Penny Haxell , Tibor Szabó

We use the abundance and weak lensing mass measurements of the SDSS maxBCG cluster catalog to simultaneously constrain cosmology and the richness--mass relation of the clusters. Assuming a flat \LambdaCDM cosmology, we find…

The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time…

Artificial Intelligence · Computer Science 2010-06-09 Junping Zhou , Minghao Yin , Chunguang Zhou

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…

Data Structures and Algorithms · Computer Science 2023-09-27 Wenjing Chen , Victoria G. Crawford

We present hardness of approximation results for Correlation Clustering with local objectives and for Hierarchical Clustering with dissimilarity information. For the former, we study the local objective of Puleo and Milenkovic (ICML '16)…

Data Structures and Algorithms · Computer Science 2020-10-06 Vaggos Chatziafratis , Neha Gupta , Euiwoong Lee

We consider the maximum weight $b$-matching problem in the random-order semi-streaming model. Assuming all weights are small integers drawn from $[1,W]$, we present a $2 - \frac{1}{2W} + \varepsilon$ approximation algorithm, using a memory…

Data Structures and Algorithms · Computer Science 2023-08-15 Chien-Chung Huang , François Sellier

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive…

Optimization and Control · Mathematics 2022-09-20 Zhuoyu Xiao , Jane J. Ye

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…

Optimization and Control · Mathematics 2023-02-15 Lennart Sinjorgo , Renata Sotirov

We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…

Data Structures and Algorithms · Computer Science 2021-08-16 Vikraman Arvind , Venkatesan Guruswami

We study the {\em maximum duo-preservation string mapping} ({\sc Max-Duo}) problem, which is the complement of the well studied {\em minimum common string partition} ({\sc MCSP}) problem. Both problems have applications in many fields…

Data Structures and Algorithms · Computer Science 2017-02-08 Yao Xu , Yong Chen , Taibo Luo , Guohui Lin

Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…

Data Structures and Algorithms · Computer Science 2022-05-24 Suprovat Ghoshal , Anand Louis

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 rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…

Data Structures and Algorithms · Computer Science 2021-12-23 Gwenaël Joret , Adrian Vetta

Fix two non-empty loopless graphs $G$ and $H$ such that $G$ maps homomorphically to $H$. The Maximum Promise Constraint Satisfaction Problem parameterised by $G$ and $H$ is the following computational problem, denoted by MaxPCSP($G$, $H$):…

Data Structures and Algorithms · Computer Science 2026-03-03 Tamio-Vesa Nakajima , Stanislav Živný

In this note, we describe a $\alpha_{GW} + \tilde{\Omega}(1/d^2)$-factor approximation algorithm for Max-Cut on weighted graphs of degree $\leq d$. Here, $\alpha_{GW}\approx 0.878$ is the worst-case approximation ratio of the…

Data Structures and Algorithms · Computer Science 2022-06-23 Jun-Ting Hsieh , Pravesh K. Kothari

The k-distance strong shortest path union cover of a graph is the minimum cardinality among all strong shortest path union cover at distance k of G. In this paper we determine the 2-strong shortest path union cover for certain graphs, also…

Combinatorics · Mathematics 2021-04-14 Antony Xavier , Santiagu Theresal , Deepa Mathew , S. Arul Amirtha Raja

In the Boolean maximum constraint satisfaction problem - Max CSP$(\Gamma)$ - one is given a collection of weighted applications of constraints from a finite constraint language $\Gamma$, over a common set of variables, and the goal is to…

Computational Complexity · Computer Science 2020-02-11 Bart M. P. Jansen , Michał Włodarczyk

Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between…

Computational Complexity · Computer Science 2018-03-20 Joshua A. Grochow , Jamie Tucker-Foltz