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We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

Discrete Mathematics · Computer Science 2012-02-06 Harold Connamacher , Michael Molloy

Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…

We study random constraint satisfaction problems (CSPs) in the unsatisfiable regime. We relate the structure of near-optimal solutions for any Max-CSP to that for an associated spin glass on the hypercube, using the Guerra-Toninelli…

Discrete Mathematics · Computer Science 2023-03-30 Chris Jones , Kunal Marwaha , Juspreet Singh Sandhu , Jonathan Shi

The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…

Data Structures and Algorithms · Computer Science 2019-08-21 Klaus Jansen , Lars Rohwedder

We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…

Computational Geometry · Computer Science 2014-04-16 Sayan Bandyapadhyay , Santanu Bhowmick , Kasturi Varadarajan

Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…

Computational Complexity · Computer Science 2012-10-17 Tomoyuki Yamakami

The fixed template Promise Constraint Satisfaction Problem (PCSP) is a recently proposed significant generalization of the fixed template CSP, which includes approximation variants of satisfiability and graph coloring problems. All the…

Computational Complexity · Computer Science 2019-09-12 Libor Barto

The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…

Data Structures and Algorithms · Computer Science 2022-03-01 Eiichiro Sato

The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases -…

Computational Complexity · Computer Science 2020-10-12 Libor Barto , Diego Battistelli , Kevin M. Berg

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…

Computational Complexity · Computer Science 2017-05-15 Sören Henning , Klaus Jansen , Malin Rau , Lars Schmarje

A $\mu$-biased Max-CSP instance with predicate $\psi:\{0,1\}^r \to \{0,1\}$ is an instance of Constraint Satisfaction Problem (CSP) where the objective is to find a labeling of relative weight at most $\mu$ which satisfies the maximum…

Data Structures and Algorithms · Computer Science 2022-01-13 Suprovat Ghoshal , Euiwoong Lee

Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…

Data Structures and Algorithms · Computer Science 2025-10-17 Noah Fleming , Yuichi Yoshida

This paper studies a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The non-renewable resource is consumed when the machine starts processing a job. We consider the…

Data Structures and Algorithms · Computer Science 2021-05-12 Susumu Hashimoto , Shinji Mizuno

Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…

Optimization and Control · Mathematics 2026-03-17 Ryan Cory-Wright , Jean Pauphilet

We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.

Data Structures and Algorithms · Computer Science 2011-01-31 Nishita Aggarwal , Naveen Garg , Swati Gupta

We study approximation algorithms for satisfiable and nearly satisfiable instances of ordering constraint satisfaction problems (ordering CSPs). Ordering CSPs arise naturally in ranking and scheduling, yet their approximability remains…

Data Structures and Algorithms · Computer Science 2026-04-01 Yury Makarychev

We build on a recently proposed method for stepwise explaining solutions of Constraint Satisfaction Problems (CSP) in a human-understandable way. An explanation here is a sequence of simple inference steps where simplicity is quantified…

Artificial Intelligence · Computer Science 2023-11-29 Emilio Gamba , Bart Bogaerts , Tias Guns

Given a fixed arity $k \geq 2$, Min-$k$-CSP on complete instances involves a set of $n$ variables $V$ and one nontrivial constraint for every $k$-subset of variables (so there are $\binom{n}{k}$ constraints). The goal is to find an…

Data Structures and Algorithms · Computer Science 2024-10-28 Aditya Anand , Euiwoong Lee , Amatya Sharma

This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has…

Numerical Analysis · Computer Science 2008-07-16 Alexandre Goldsztejn , Claude Michel , Michel Rueher

We give an approximation algorithm for Quantum Max-Cut which works by rounding an SDP relaxation to an entangled quantum state. The SDP is used to choose the parameters of a variational quantum circuit. The entangled state is then…

Quantum Physics · Physics 2023-11-15 Robbie King