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Electronic Colloquium on Computational Complexity

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Reports tagged with optimization:
TR96-028 | 9th April 1996
Sanjeev Khanna, Madhu Sudan

The Optimization Complexity of Constraint Satisfaction Problems

In 1978, Schaefer considered a subclass of languages in
NP and proved a ``dichotomy theorem'' for this class. The subclass
considered were problems expressible as ``constraint satisfaction
problems'', and the ``dichotomy theorem'' showed that every language in
this class is either in P, or is NP-hard. This result is in ... more >>>

TR97-025 | 26th May 1997
Harald Hempel, Gerd Wechsung

The Operators min and max on the Polynomial Hierarchy

We define a general maximization operator max and a general minimization
operator min for complexity classes and study the inclusion structure of
the classes max.P, max.NP, max.coNP, min.P, min.NP, and min.coNP.
It turns out that Krentel's class OptP fits naturally into this frame-
work (it can be ... more >>>

TR98-008 | 15th January 1998
Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, Mario Szegedy

Proof verification and the hardness of approximation problems.

We show that every language in NP has a probablistic verifier
that checks membership proofs for it using
logarithmic number of random bits and by examining a
<em> constant </em> number of bits in the proof.
If a string is in the language, then there exists a proof ... more >>>

TR98-022 | 14th April 1998
Steffen Reith, Heribert Vollmer

The Complexity of Computing Optimal Assignments of Generalized Propositional Formulae

We consider the problems of finding the lexicographically
minimal (or maximal) satisfying assignment of propositional
formulae for different restricted formula classes. It turns
out that for each class from our framework, the above problem
is either polynomial time solvable or complete for ... more >>>

TR98-034 | 23rd June 1998
Venkatesan Guruswami, Daniel Lewin and Madhu Sudan, Luca Trevisan

A tight characterization of NP with 3 query PCPs

It is known that there exists a PCP characterization of NP
where the verifier makes 3 queries and has a {\em one-sided}
error that is bounded away from 1; and also that 2 queries
do not suffice for such a characterization. Thus PCPs with
3 ... more >>>

TR98-040 | 24th July 1998
Madhu Sudan, Luca Trevisan

Probabilistically checkable proofs with low amortized query complexity

The error probability of Probabilistically Checkable Proof (PCP)
systems can be made exponentially small in the number of queries
by using sequential repetition. In this paper we are interested
in determining the precise rate at which the error goes down in
an optimal protocol, and we make substantial progress toward ... more >>>

TR02-030 | 3rd June 2002
Lars Engebretsen, Jonas Holmerin, Alexander Russell

Inapproximability Results for Equations over Finite Groups

Revisions: 1

An equation over a finite group G is an expression of form
w_1 w_2...w_k = 1_G, where each w_i is a variable, an inverted
variable, or a constant from G; such an equation is satisfiable
if there is a setting of the variables to values in G ... more >>>

TR03-048 | 24th June 2003
Stefan Droste, Thomas Jansen, Ingo Wegener

Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

Randomized search heuristics like local search, simulated annealing or all kinds of evolutionary algorithms have many applications. However, for most problems the best worst-case expected run times are achieved by more problem-specific algorithms. This raises the question about the limits of general randomized search heuristics.

Here a framework called black-box ... more >>>

TR03-077 | 4th September 2003
Till Tantau

Logspace Optimisation Problems and their Approximation Properties

This paper introduces logspace optimisation problems as
analogues of the well-studied polynomial-time optimisation
problems. Similarly to them, logspace
optimisation problems can have vastly different approximation
properties, even though the underlying existence and budget problems
have the same computational complexity. Numerous natural problems
are presented that exhibit such a varying ... more >>>

TR08-044 | 2nd April 2008
Miki Hermann, Reinhard Pichler

Complexity of Counting the Optimal Solutions

Following the approach of Hemaspaandra and Vollmer, we can define
counting complexity classes #.C for any complexity class C of decision
problems. In particular, the classes #.Pi_{k}P with k >= 1
corresponding to all levels of the polynomial hierarchy have thus been
studied. However, for a large variety of counting ... more >>>

TR12-009 | 28th November 2011
Prabhu Manyem, Julien Ugon

Computational Complexity, NP Completeness and Optimization Duality: A Survey

We survey research that studies the connection between the computational complexity
of optimization problems on the one hand, and the duality gap between the primal and
dual optimization problems on the other. To our knowledge, this is the first survey that
connects the two very important areas. We further look ... more >>>

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