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- Hans Kleine Büning, Marek Karpinski, Andreas Flögel
- Inf. Comput.
- 1995

- Piotr Berman, Moses Charikar, Marek Karpinski
- Electronic Colloquium on Computational Complexity
- 1997

We consider the problem of scheduling permanent jobs on related machines in an on-line fashion. We design a new algorithm that achieves the competitive ratio of 3+ p 8 5:828 for the deterministic version, and 3:31= ln 2:155 4:311 for its randomized variant, improving the previous competitive ratios of 8 and 2e 5:436. We also prove lower bounds of 2:4380 on… (More)

- Sanjeev Arora, David R. Karger, Marek Karpinski
- STOC
- 1995

We present a uniied framework for designing polynomial time approximationschemes (PTASs) for \dense" instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation , minimumk-way cut with and without speciied sources, and maximum 3-satissability. Dense graphs for us are graphs with minimumdegree (n), although some… (More)

- Piotr Berman, Marek Karpinski
- Electronic Colloquium on Computational Complexity
- 1998

We prove a number of improved inaproximability results, including the best up to date explicit approximation thresholds for MIS problem of bounded degree, bounded occurrences MAX-2SAT, and bounded degree Node Cover. We prove also for the rst time inapproxima-bility of the problem of Sorting by Reversals and display an explicit approximation threshold. This… (More)

- Piotr Berman, Sridhar Hannenhalli, Marek Karpinski
- Electronic Colloquium on Computational Complexity
- 1998

A reversal on a permutation of (1,.. . , n} is a transformation that reverses the order of a block of two or more consecutive elements of the permutation. The problem of determining the smallest number of reversals required to transform a given permutation to the identity (or to sort the permutation by reversals) has been shown to be NP-hard. In this paper… (More)

- Marek Karpinski, Alex Zelikovsky
- Electronic Colloquium on Computational Complexity
- 1995

The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of… (More)

- Marek Karpinski, Angus Macintyre
- STOC
- 1994

We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the rst time, the VC Dimension of analog neural networks with the sigmoid activation function (y) = 1=1 + e ?y to be bounded by a quadratic polynomial in the number of programmable parameters.

- Piotr Berman, Marek Karpinski, Alex D. Scott
- Electronic Colloquium on Computational Complexity
- 2003

- Piotr Berman, Marek Karpinski
- ICALP
- 1999