Related papers: Statistical Physics of Hard Optimization Problems
This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical…
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of…
The quantified constraint satisfaction problem (QCSP) is a powerful framework for modelling computational problems. The general intractability of the QCSP has motivated the pursuit of restricted cases that avoid its maximal complexity. In…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
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…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…
We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the…
We study the computational complexity of scheduling jobs on a single speed-scalable processor with the objective of capturing the trade-off between the (weighted) flow time and the energy consumption. This trade-off has been extensively…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
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,…
We consider a high-dimensional random constrained optimization problem in which a set of binary variables is subjected to a linear system of equations. The cost function is a simple linear cost, measuring the Hamming distance with respect…