TY - GEN

T1 - Approximation hardness of bounded degree MIN-CSP and MIN-BISECTION

AU - Berman, Piotr

AU - Karpinski, Marek

PY - 2002

Y1 - 2002

N2 - We consider bounded occurrence (degree) instances of a minimum constraint satisfaction problem MIN-LIN2 and a MINBISECTION problem for graphs. MIN-LIN2 is an optimization problem for a given system of linear equations mod 2 to construct a solution that satisfies the minimum number of them. E3-OCC-MIN-E3-LIN2 is the bounded occurrence (degree) problem restricted as follows: each equation has exactly 3 variables and each variable occurs in exactly 3 equations. Clearly, MIN-LIN2 is equivalent to another well known problem, the Nearest Codeword problem, and E3-OCC-MIN-E3-LIN2 to its bounded occurrence version. MIN-BISECTION is a problem of findinga minimum bisection of a graph, while 3-MIN-BISECTION is the MIN-BISECTION problem restricted to 3-regular graphs only. We show that, somewhat surprisingly, these two restricted problems are exactly as hard to approximate as their general versions. In particular, an approximation ratio lower bound for E3-OCC-MIN-E3-LIN2 (bounded 3-occurrence 3-ary Nearest Codeword problem) is equal to MIN-LIN2 (Nearest Codeword problem) lower bound nΩ(1)/ log log n. Moreover, an existence of a constant factor approximation ratio (or a PTAS) for 3-MIN-BISECTION entails existence of a constant approximation ratio (or a PTAS) for the general MIN-BISECTION.

AB - We consider bounded occurrence (degree) instances of a minimum constraint satisfaction problem MIN-LIN2 and a MINBISECTION problem for graphs. MIN-LIN2 is an optimization problem for a given system of linear equations mod 2 to construct a solution that satisfies the minimum number of them. E3-OCC-MIN-E3-LIN2 is the bounded occurrence (degree) problem restricted as follows: each equation has exactly 3 variables and each variable occurs in exactly 3 equations. Clearly, MIN-LIN2 is equivalent to another well known problem, the Nearest Codeword problem, and E3-OCC-MIN-E3-LIN2 to its bounded occurrence version. MIN-BISECTION is a problem of findinga minimum bisection of a graph, while 3-MIN-BISECTION is the MIN-BISECTION problem restricted to 3-regular graphs only. We show that, somewhat surprisingly, these two restricted problems are exactly as hard to approximate as their general versions. In particular, an approximation ratio lower bound for E3-OCC-MIN-E3-LIN2 (bounded 3-occurrence 3-ary Nearest Codeword problem) is equal to MIN-LIN2 (Nearest Codeword problem) lower bound nΩ(1)/ log log n. Moreover, an existence of a constant factor approximation ratio (or a PTAS) for 3-MIN-BISECTION entails existence of a constant approximation ratio (or a PTAS) for the general MIN-BISECTION.

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U2 - 10.1007/3-540-45465-9_53

DO - 10.1007/3-540-45465-9_53

M3 - Conference contribution

AN - SCOPUS:84869192673

SN - 3540438645

SN - 9783540438649

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

SP - 623

EP - 632

BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings

A2 - Widmayer, Peter

A2 - Eidenbenz, Stephan

A2 - Triguero, Francisco

A2 - Morales, Rafael

A2 - Conejo, Ricardo

A2 - Hennessy, Matthew

PB - Springer Verlag

T2 - 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002

Y2 - 8 July 2002 through 13 July 2002

ER -