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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > ALGORITHMS:
Reports tagged with algorithms:
TR95-022 | 2nd May 1995
Marek Karpinski, Wojciech Rytter, Ayumi Shinohara

Pattern-Matching for Strings with Short Descriptions

We consider strings which are succinctly described. The description
is in terms of straight-line programs in which the constants are
symbols and the only operation is the concatenation. Such
descriptions correspond to the systems of recurrences or to
context-free grammars generating single words. The descriptive ... more >>>


TR98-012 | 2nd February 1998
Meena Mahajan, V Vinay

Determinant: Old Algorithms, New Insights


In this paper we approach the problem of computing the characteristic
polynomial of a matrix from the combinatorial viewpoint. We present
several combinatorial characterizations of the coefficients of the
characteristic polynomial, in terms of walks and closed walks of
different kinds in the underlying graph. We develop algorithms based
more >>>


TR98-043 | 27th July 1998
Venkatesan Guruswami, Madhu Sudan

Improved decoding of Reed-Solomon and algebraic-geometric codes.

We present an improved list decoding algorithm for decoding
Reed-Solomon codes. Given an arbitrary string of length n, the
list decoding problem is that of finding all codewords within a
specified Hamming distance from the input string.

It is well-known that this decoding problem for Reed-Solomon
codes reduces to the ... more >>>


TR98-062 | 28th October 1998
Oded Goldreich, Dana Ron, Madhu Sudan

Chinese Remaindering with Errors

Revisions: 4 , Comments: 1

The Chinese Remainder Theorem states that a positive
integer m is uniquely specified by its remainder modulo
k relatively prime integers p_1,...,p_k, provided
m < \prod_{i=1}^k p_i. Thus the residues of m modulo
relatively prime integers p_1 < p_2 < ... < p_n
form a redundant representation of m if ... more >>>


TR01-092 | 2nd October 2001
Till Tantau

A Note on the Complexity of the Reachability Problem for Tournaments

Deciding whether a vertex in a graph is reachable from another
vertex has been studied intensively in complexity theory and is
well understood. For common types of graphs like directed graphs,
undirected graphs, dags or trees it takes a (possibly
nondeterministic) logspace machine to decide the reachability
problem, and ... more >>>


TR04-039 | 21st April 2004
Andrzej Lingas, Martin Wahlén

On approximation of the maximum clique minor containment problem and some subgraph homeomorphism problems

We consider the ``minor'' and ``homeomorphic'' analogues of the maximum clique problem, i.e., the problems of determining the largest $h$ such that the input graph has a minor isomorphic to $K_h$ or a subgraph homeomorphic to $K_h,$ respectively.We show the former to be approximable within $O(\sqrt {n} \log^{1.5} n)$ by ... more >>>


TR05-103 | 17th August 2005
Leonid Gurvits

A proof of hyperbolic van der Waerden conjecture : the right generalization is the ultimate simplification

Consider a homogeneous polynomial $p(z_1,...,z_n)$ of degree $n$ in $n$ complex variables .
Assume that this polynomial satisfies the property : \\

$|p(z_1,...,z_n)| \geq \prod_{1 \leq i \leq n} Re(z_i)$ on the domain $\{(z_1,...,z_n) : Re(z_i) \geq 0 , 1 \leq i \leq n \}$ . \\

We prove that ... more >>>


TR06-029 | 21st February 2006
Diptarka Chakraborty, Nikhil R. Devanur, Vijay V. Vazirani

Eisenberg-Gale Markets: Rationality, Strongly Polynomial Solvability, and Competition Monotonicity

We study the structure of EG[2], the class of Eisenberg-Gale markets
with two agents. We prove that all markets in this class are rational and they
admit strongly polynomial algorithms whenever
the polytope containing the set of feasible utilities of the two agents can be described
via a combinatorial LP. ... more >>>


TR07-017 | 18th January 2007
Ashish Rastogi, Richard Cole

Indivisible Markets with Good Approximate EquilibriumPrices

Revisions: 1

This paper considers the tradeoff between divisibility and the hardness of approximating
equilibrium prices. Tight bounds are obtained for smooth Fisher markets that obey a relaxed
weak gross substitutes property (WGS). A smooth market is one in which small changes in
prices cause only proportionately small changes ... more >>>


TR13-117 | 1st September 2013
Igor Oliveira

Algorithms versus Circuit Lower Bounds

Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how circuit lower bounds can be obtained from derandomization, compression, learning, and satisfiability ... more >>>




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