TY - GEN

T1 - Probabilistic approximation of some NP optimization problems by finite-state machines

AU - Hong, Dawei

AU - Birget, Jean Camille

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 1997.

PY - 1997

Y1 - 1997

N2 - We introduce a subclass of NP optimization problems which contains, e.g., Bin Covering and Bin Packing. For each problem in this subclass we prove that with probability tending to 1 as the number of input items tends to infinity, the problem is approximable up to any given constant factor ε > 0 by a finite-state machine. More precisely, let II be a problem in our subclass of NP optimization problems, and let I be an input represented by a sequence of n independent identically distributed random variables with a fixed distribution. Then for any ε > 0 there exists a finite-state machine which does the following: On a random input I the finite-state machine produces a feasible solution whose objective value M(I) satisfies (Formula Presented)when n is large enough. Here K and h are positive constants.

AB - We introduce a subclass of NP optimization problems which contains, e.g., Bin Covering and Bin Packing. For each problem in this subclass we prove that with probability tending to 1 as the number of input items tends to infinity, the problem is approximable up to any given constant factor ε > 0 by a finite-state machine. More precisely, let II be a problem in our subclass of NP optimization problems, and let I be an input represented by a sequence of n independent identically distributed random variables with a fixed distribution. Then for any ε > 0 there exists a finite-state machine which does the following: On a random input I the finite-state machine produces a feasible solution whose objective value M(I) satisfies (Formula Presented)when n is large enough. Here K and h are positive constants.

KW - Approximation

KW - Finite-state machines

KW - NP- optimization problems

KW - Probabilistic algorithms

UR - http://www.scopus.com/inward/record.url?scp=84957626112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957626112&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/3-540-63248-4_13

DO - https://doi.org/10.1007/3-540-63248-4_13

M3 - Conference contribution

SN - 3540632484

SN - 9783540632481

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 151

EP - 164

BT - Randomization and Approximation Techniques in Computer Science - International Workshop, RANDOM 1997, Proceedings

A2 - Rolim, José

PB - Springer Verlag

T2 - International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 1997

Y2 - 11 July 1997 through 12 July 1997

ER -