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Electronic Colloquium on Computational Complexity

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All reports by Author Michael Alekhnovich:

TR09-038 | 14th April 2009
Michael Alekhnovich, Allan Borodin, Joshua Buresh-Oppenheim, Russell Impagliazzo, Avner Magen

Toward a Model for Backtracking and Dynamic Programming

We propose a model called priority branching trees (pBT ) for backtracking and dynamic
programming algorithms. Our model generalizes both the priority model of Borodin, Nielson
and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence
spans a wide spectrum of algorithms. After witnessing the ... more >>>

TR04-117 | 1st December 2004
Michael Alekhnovich, Sanjeev Arora, Iannis Tourlakis

Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy

Lovasz and Schrijver described a generic method of tightening the LP and SDP relaxation for any 0-1 optimization problem. These tightened relaxations were the basis of several celebrated approximation algorithms (such as for MAX-CUT, MAX-3SAT, and SPARSEST CUT).

We prove strong nonapproximability results in this model for well-known problems such ... more >>>

TR04-041 | 18th May 2004
Michael Alekhnovich, Edward Hirsch, Dmitry Itsykson

Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas

DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satisfiability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatisfiable formulas are equivalent to tree-like resolution proofs. Therefore, lower bounds for tree-like resolution (which ... more >>>

TR04-016 | 3rd March 2004
Michael Alekhnovich, Eli Ben-Sasson

Linear Upper Bounds for Random Walk on Small Density Random 3CNFs

We analyze the efficiency of the random walk algorithm on random 3CNF instances, and prove em linear upper bounds on the running time
of this algorithm for small clause density, less than 1.63. Our upper bound matches the observed running time to within a multiplicative factor. This is the ... more >>>

TR01-056 | 6th August 2001
Michael Alekhnovich, Jan Johannsen, Alasdair Urquhart

An Exponential Separation between Regular and General Resolution

This paper gives two distinct proofs of an exponential separation
between regular resolution and unrestricted resolution.
The previous best known separation between these systems was

more >>>

TR00-023 | 11th May 2000
Michael Alekhnovich, Eli Ben-Sasson, Alexander Razborov, Avi Wigderson

Pseudorandom Generators in Propositional Proof Complexity

We call a pseudorandom generator $G_n:\{0,1\}^n\to \{0,1\}^m$ {\em
hard} for a propositional proof system $P$ if $P$ can not efficiently
prove the (properly encoded) statement $G_n(x_1,\ldots,x_n)\neq b$ for
{\em any} string $b\in\{0,1\}^m$. We consider a variety of
``combinatorial'' pseudorandom generators inspired by the
Nisan-Wigderson generator on the one hand, and ... more >>>

TR99-040 | 20th October 1999
Michael Alekhnovich, Eli Ben-Sasson, Alexander Razborov, Avi Wigderson

Space Complexity in Propositional Calculus

We study space complexity in the framework of
propositional proofs. We consider a natural model analogous to
Turing machines with a read-only input tape, and such
popular propositional proof systems as Resolution, Polynomial
Calculus and Frege systems. We propose two different space measures,
corresponding to the maximal number of bits, ... more >>>

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