2-Way vs. d-Way Branching for CSP

نویسندگان

  • Joey Hwang
  • David G. Mitchell
چکیده

Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple “branching schemes”: 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying two variants of the resolution proof system, denoted C-RES and NG-RES , which model the reasoning of CSP algorithms. The tree-like restrictions, tree-C-RES and tree-NG-RES , exactly capture the power of backtracking with 2-way branching and d-way branching, respectively. We give a family instances which require exponential sized search trees for backtracking with d-way branching, but have size O(dn) search trees for backtracking with 2way branching. We also give a natural branching strategy with which backtracking with 2-way branching finds refutations of these instances in time O(dn). The unrestricted variants of C-RES and NG-RES can simulate the reasoning of algorithms which incorporate learning and k-consistency enforcement. We show exponential separations between C-RES and NG-RES , as well as between the tree-like and unrestricted versions of each system. All separations given are nearly optimal.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Resolution and Constraint Satisfaction

We study two resolution-like refutation systems for finitedomain constraint satisfaction problems, and the efficiency of these and of common CSP algorithms. By comparing the relative strength of these systems, we show that for instances with domain size d, backtracking with 2-way branching is super-polynomially more powerful than backtracking with d-way branching. We compare these systems with ...

متن کامل

Experimental Evaluation of Branching Schemes for the CSP

The search strategy of a CP solver is determined by the variable and value ordering heuristics it employs and by the branching scheme it follows. Although the effects of variable and value ordering heuristics on search effort have been widely studied, the effects of different branching schemes have received less attention. In this paper we study this effect through an experimental evaluation th...

متن کامل

Adaptive Branching for Constraint Satisfaction Problems

The two standard branching schemes for CSPs are d-way and 2-way branching. Although it has been shown that in theory the latter can be exponentially more effective than the former, there is a lack of empirical evidence showing such differences. To investigate this, we initially make an experimental comparison of the two branching schemes over a wide range of benchmarks. Experimental results ver...

متن کامل

-angelic Choice for Process Algebra

The-angelic choice is an operator that captures the behaviour of the external choice of CSP in a branching time setting. The idea of the-angelic choice is to delay any choice until an observable action happens. In this way, this new operator avoids preemption introduced by internal actions (actions). It is studied in theories with abstraction, more precisely, branching bisimulation and-bisimula...

متن کامل

-angelic choice: An operator to reduce irrelevant internal activity in process algebra

The-angelic choice is an operator that captures the behaviour of the external choice of CSP in a branching time setting. The idea of the-angelic choice is to delay any choice until an observable action happens. In this way, this new operator avoids preemption introduced by internal actions (actions). It is studied in theories with abstraction, more precisely, branching bisimulation and-bisimula...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005