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We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions.…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
Several fragments of the satisfiability problem have been studied in the literature. Among these, Linear 3-SAT is a satisfaction problem in which each clause (viewed as a set of literals) intersects with at most one other clause; moreover,…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
Global constraints proved themselves to be an efficient tool for modelling and solving large-scale real-life combinatorial problems. They encapsulate a set of binary constraints and using global reasoning about this set they filter the…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
This paper addresses the problem of collaboratively satisfying long-term spatial constraints in multi-agent systems. Each agent is subject to spatial constraints, expressed as inequalities, which may depend on the positions of other agents…
Distributed Constraint Satisfaction (DCSP) has long been considered an important problem in multi-agent systems research. This is because many real-world problems can be represented as constraint satisfaction and these problems often…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
We describe an extensive study of search in GSAT, an approximation procedure for propositional satisfiability. GSAT performs greedy hill-climbing on the number of satisfied clauses in a truth assignment. Our experiments provide a more…
The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT…
This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this…