Strategies for Solving SAT in Grids by Randomized Search

Abstract

Abstract. Grid computing offers a promising approach to solving challenging computational problems in an environment consisting of a large number of easily accessible resources. In this paper we develop strategies for solving collections of hard instances of the propositional satisfiability problem (SAT) with a randomized SAT solver run in a Grid. We study alternative strategies by using a simulation framework which is composed of (i) a grid model capturing the communication and management delays, and (ii) run-time distributions of a randomized solver, obtained by running a state-of-the-art SAT solver on a collection of hard instances. The results are experimentally validated in a production level Grid. When solving a single hard SAT instance, the results show that in practice only a relatively small amount of parallelism can be efficiently used; the speedup obtained by increasing parallelism thereafter is negligible. This observation leads to a novel strategy of using grid to solve collections of hard instances. Instead of solving instances one-by-one, the strategy aims at decreasing the overall solution time by applying an alternating distribution schedule.

A survey of SAT solver

“…In [23], MiniSAT1.14 with multiple different restart strategies is executed in the grid, each node is independent and there is no communication between the nodes. This approach can solve multiple instances of SAT at the same time, but does not achieve super-linear acceleration effect.…”

Partitioning SAT Instances for Distributed Solving

“…Firstly, it is of course problematic to determine the value for n. Secondly, a more subtle problem is that if no guarantees can be given on the run times of the derived instances and the instance to be solved is unsatisfiable, increasing n arbitrarily might increase the expected run time. We call a badly working partition function, which results in derived instances with run times equal to that of the original instance, a void partition function 1 . Void partition functions are especially harmful for proving unsatisfiability, since it is not possible to obtain any speedup with a void partition function in plain partitioning [12]: Proposition 1.…”

“…The goal can be straightforwardly achieved by exploiting the randomized nature of current state-of-the-art SAT solvers with the simple distribution (SD) approach, where one just runs a randomized solver a number of times independently. This leads to surprisingly good speed-ups even in a grid environment with substantial communication and other delays [1]. The approach could be extended by applying particular restart strategies [2,3] or employing an algorithm portfolio scheme [4,5].…”

Incorporating Learning in Grid-Based Randomized SAT Solving

“…For a more detailed analysis of running randomized SAT solvers in a parallel, distributed environment involving communication and other delays, see e.g. [7]. Although this simple strategy of running randomized SAT solvers in parallel, which we call the Simple Distributed SAT solving (SDSAT) approach, can reduce the expected time to solve an instance, it cannot reduce it below the minimum running time (i.e.…”

“…Firstly, some problems, such as vmpc_33, are solved in less than one hour with the CL-SDSAT prototype and are, thus, clearly also solvable with the basic SDSAT method [7] with no parallel clause learning. Secondly, and more importantly, the prototype solves, with one hour time limit for each job, several problems which were not solved by any solver in SAT 2007 competition in 10,000 seconds.…”