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In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…

Artificial Intelligence · Computer Science 2025-09-24 Pierre Montalbano , Simon de Givry , George Katsirelos

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

Machine Learning · Statistics 2017-10-04 Kinjal Basu , Ankan Saha , Shaunak Chatterjee

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…

Data Structures and Algorithms · Computer Science 2024-08-06 Zongchen Chen , Andreas Galanis , Leslie Ann Goldberg , Heng Guo , Andrés Herrera-Poyatos , Nitya Mani , Ankur Moitra

Recently a strong connection has been shown between the tractability of integer programming (IP) with bounded coefficients on the one side and the structure of its constraint matrix on the other side. To that end, integer linear programming…

Computational Complexity · Computer Science 2020-12-02 Eduard Eiben , Robert Ganian , Dušan Knop , Sebastian Ordyniak , Michał Pilipczuk , Marcin Wrochna

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

Parametric path problems arise independently in diverse domains, ranging from transportation to finance, where they are studied under various assumptions. We formulate a general path problem with relaxed assumptions, and describe how this…

Data Structures and Algorithms · Computer Science 2021-06-08 Prerona Chatterjee , Kshitij Gajjar , Jaikumar Radhakrishnan , Girish Varma

We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…

Optimization and Control · Mathematics 2014-12-02 Evgeny Shindin , Gideon Weiss

The class $(r,2)$-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two $r$-valued variables per clause. For instances with $n$ variables and $m$ binary clauses, we present an $O(n r^{5+19m/100})$-time…

Discrete Mathematics · Computer Science 2008-03-26 Alexander D. Scott , Gregory B. Sorkin

This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…

Data Structures and Algorithms · Computer Science 2014-02-04 Evan A. Sultanik

We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…

Probability · Mathematics 2011-11-10 Bela Bollobas , Svante Janson , Oliver Riordan

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

Computational Complexity · Computer Science 2018-01-31 Giacomo Patrizi

In a recent line of work, Butti and Dalmau have shown that a fixed-template Constraint Satisfaction Problem is solvable by a certain natural linear programming relaxation (equivalent to the basic linear programming relaxation) if and only…

Data Structures and Algorithms · Computer Science 2022-05-11 Libor Barto , Silvia Butti

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

A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is…

Disordered Systems and Neural Networks · Physics 2009-11-11 Olivier Rivoire , Julien Barré

We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…

Data Structures and Algorithms · Computer Science 2025-05-20 Shi Li , Chenyang Xu , Ruilong Zhang

Clique tree conversion solves large-scale semidefinite programs by splitting an $n\times n$ matrix variable into up to $n$ smaller matrix variables, each representing a principal submatrix of up to $\omega\times\omega$. Its fundamental…

Optimization and Control · Mathematics 2020-05-26 Richard Y. Zhang , Javad Lavaei

A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…

Machine Learning · Computer Science 2014-12-30 Daniil Ryabko

Constraint Satisfaction Problem (CSP) is a framework for modeling and solving a variety of real-world problems. Once the problem is expressed as a finite set of constraints, the goal is to find the variables' values satisfying them. Even…

Discrete Mathematics · Computer Science 2019-05-23 Rachid Oucheikh , Ismail Berrada , Outman El Hichami

This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly…

Optimization and Control · Mathematics 2021-09-29 Jose E. Ramirez-Calderon , V. Jorge Leon

We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…

Logic in Computer Science · Computer Science 2007-05-23 Randal E. Bryant , Miroslav N. Velev