TY - GEN

T1 - On the hardness of approximating NP witnesses

AU - Feige, Uriel

AU - Langberg, Michael

AU - Nissim, Kobbi

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The search version for NP-complete combinatorial optimization problems asks for finding a solution of optimal value. Such a solution is called a witness. We follow a recent paper by Kumar and Sivakumar, and study a relatively new notion of approximate solutions that ignores the value of a solution and instead considers its syntactic representation (under some standard encoding scheme). The results that we present are of a negative nature. We show that for many of the well known NP-complete problems (such as 3-SAT, CLIQUE, 3-COLORING, SET COVER) it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution. In fact, we have been able to show similar results for most of Karp’s 21 original NP-complete problems. (At the moment, our results are not tight only for UNDIRECTED HAMILTONIAN CYCLE and FEEDBACK EDGE SET).

AB - The search version for NP-complete combinatorial optimization problems asks for finding a solution of optimal value. Such a solution is called a witness. We follow a recent paper by Kumar and Sivakumar, and study a relatively new notion of approximate solutions that ignores the value of a solution and instead considers its syntactic representation (under some standard encoding scheme). The results that we present are of a negative nature. We show that for many of the well known NP-complete problems (such as 3-SAT, CLIQUE, 3-COLORING, SET COVER) it is NP-hard to produce a solution whose Hamming distance from an optimal solution is substantially closer than what one would obtain by just taking a random solution. In fact, we have been able to show similar results for most of Karp’s 21 original NP-complete problems. (At the moment, our results are not tight only for UNDIRECTED HAMILTONIAN CYCLE and FEEDBACK EDGE SET).

UR - http://www.scopus.com/inward/record.url?scp=84937424609&partnerID=8YFLogxK

U2 - 10.1007/3-540-44436-x_13

DO - 10.1007/3-540-44436-x_13

M3 - Conference contribution

AN - SCOPUS:84937424609

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

SP - 120

EP - 131

BT - Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings

A2 - Jansen, Klaus

A2 - Khuller, Samir

PB - Springer Verlag

T2 - 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000

Y2 - 5 September 2000 through 8 September 2000

ER -