TY - JOUR

T1 - Dissection

T2 - A new paradigm for solving bicomposite search problems

AU - Dinur, Itai

AU - Dunkelman, Orr

AU - Keller, Nathan

AU - Shamir, Adi

N1 - Publisher Copyright:
© 2014 ACM 0001-0782/14/10 $15.00.

PY - 2014/9/23

Y1 - 2014/9/23

N2 - Combinatorial search problems are usually described by a collection of possible states, a list of possible actions which map each current state into some next state, and a pair of initial and final states. The algorithmic problem is to find a sequence of actions which maps the given initial state into the desired final state. In this paper, we introduce the new notion of bicomposite search problems, and show that they can be solved with improved combinations of time and space complexities by using a new algorithmic paradigm called dissection. To demonstrate the broad applicability of our new paradigm, we show how to use it in order to untangle Rubik's cube and to solve a typical NP-complete partition problem with algorithms which are better than any previously described algorithm for these problems.

AB - Combinatorial search problems are usually described by a collection of possible states, a list of possible actions which map each current state into some next state, and a pair of initial and final states. The algorithmic problem is to find a sequence of actions which maps the given initial state into the desired final state. In this paper, we introduce the new notion of bicomposite search problems, and show that they can be solved with improved combinations of time and space complexities by using a new algorithmic paradigm called dissection. To demonstrate the broad applicability of our new paradigm, we show how to use it in order to untangle Rubik's cube and to solve a typical NP-complete partition problem with algorithms which are better than any previously described algorithm for these problems.

UR - http://www.scopus.com/inward/record.url?scp=84908236622&partnerID=8YFLogxK

U2 - 10.1145/2661434

DO - 10.1145/2661434

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AN - SCOPUS:84908236622

SN - 0001-0782

VL - 57

SP - 98

EP - 105

JO - Communications of the ACM

JF - Communications of the ACM

IS - 10

ER -