Solving Strategies for Highly Symmetric CSPs

This paper is organized as follows. In Section 2, we introduce some basic concepts. In Section 3, we explain two strategies for symmetry exploitation during search. In Section 4, we present the problem of B I B D generation. In Section 5, we formulate the B I B D generation as a CSP and give empirical results. In Section 6, we revise previous approaches to this topic. Section 7 contains conclusions and future work. 2 Basic De f in i t i ons C o n s t r a i n t sa t i s f ac t i on . A finite CSP is defined by a tr iple (X ' ,D ,C) , where ,V = is a set of n variables, V = is a collection of current domains where is the finite set of possible values for variable , and C is a set. of constraints among variables, A constraint C i on the ordered set of variables specifies the relation of the allowed combinations of values for the variables in var An element of is a tuple , where represents the in i t ia l domain of . An element of is called a valid tuple on var A solution of the CSP is an assignment of values to variables which satisfies every constraint. A value a is good for a variable if a solution includes the assignment Typical ly, CSPs are solved by depth-first search algorithms wi th backtracking. At a point in search, P is the set of assigned or past variables, and F is the set of unassigned or future variables. The variable to be assigned next is called the current variable. S y m m e t r i e s . A symmetry on a CSP is a collection of bijective mappings 400 CONSTRAINT SATISFACTION Solving Strategies for H igh l y Symmetr ic CSPs * Pedro Meseguer Ca rme Torras Inst. Invest. Intel.ligencia Artificial Inst. Robotica i Informatica Industrial CSIC CSIC-UPC Campus UAB, 08193 Bellaterra Gran Capita 2-4, 08034 Barcelona Spain Spain