25 research outputs found
On solving distributed CS(O)Ps with privacy
Cryptographic protocols can enforce privacy in distributed computation of functions [Goldwasser'96] and are a competitor of the distributed constructive search techniques. [Goldreich'87,Chaum'87,Chaum'88,Ben-or'88] show how cryptographic protocols can be compiled from protocols/functions for honest agents. For some combinations of concepts of security and types of attacks, cryptographic protocols obtained this way can be safe. We discuss their application to constraint satisfaction (and optimization) problems. A first version of this report, with some notation problems, appears in the PhD thesis report [Silaghi'02]
Branch-and-Prune Search Strategies for Numerical Constraint Solving
When solving numerical constraints such as nonlinear equations and
inequalities, solvers often exploit pruning techniques, which remove redundant
value combinations from the domains of variables, at pruning steps. To find the
complete solution set, most of these solvers alternate the pruning steps with
branching steps, which split each problem into subproblems. This forms the
so-called branch-and-prune framework, well known among the approaches for
solving numerical constraints. The basic branch-and-prune search strategy that
uses domain bisections in place of the branching steps is called the bisection
search. In general, the bisection search works well in case (i) the solutions
are isolated, but it can be improved further in case (ii) there are continuums
of solutions (this often occurs when inequalities are involved). In this paper,
we propose a new branch-and-prune search strategy along with several variants,
which not only allow yielding better branching decisions in the latter case,
but also work as well as the bisection search does in the former case. These
new search algorithms enable us to employ various pruning techniques in the
construction of inner and outer approximations of the solution set. Our
experiments show that these algorithms speed up the solving process often by
one order of magnitude or more when solving problems with continuums of
solutions, while keeping the same performance as the bisection search when the
solutions are isolated.Comment: 43 pages, 11 figure
Secure Multi-party Computation for selecting a solution according to a uniform distribution over all solutions of a general combinatorial problem
Secure simulations of arithmetic circuit and boolean circuit evaluations are known to save privacy while providing solutions to any probabilistic function over a field. The problem we want to solve is to select a random solution of a general combinatorial problem. Here we discuss how to specify the need of selecting a random solution of a general combinatorial problem, as a probabilistic function. Arithmetic circuits for finding the set of all solutions are simple to design [24]