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Electronic Colloquium on Computational Complexity

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All reports by Author Piotr Berman:

TR08-094 | 10th October 2008
Piotr Berman, Marek Karpinski, Alexander Zelikovsky

1.25 Approximation Algorithm for the Steiner Tree Problem with Distances One and Two

We give a 1.25 approximation algorithm for the Steiner Tree Problem with distances one and two, improving on the best known bound for that problem.

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TR07-119 | 5th December 2007
Piotr Berman, Bhaskar DasGupta, Marek Karpinski

Approximating Transitive Reductions for Directed Networks

We consider <i>minimum equivalent digraph</i> (<i>directed network</i>) problem (also known as the <i>strong transitive reduction</i>), its maximum optimization variant, and some extensions of those two types of problems. We prove the existence of polynomial time approximation algorithms with ratios 1.5 for all the minimization problems and 2 for all the ... more >>>

TR07-092 | 10th July 2007
Piotr Berman, Bhaskar DasGupta

Approximating the Online Set Multicover Problems Via Randomized Winnowing

In this paper, we consider the weighted online set k-multicover problem. In this problem, we have an universe V of elements, a family SS of subsets of V with a positive real cost for every S\in SS, and a ``coverage factor'' (positive integer) k. A subset \{i_0,i_1,\ldots\ \subseteq V of ... more >>>

TR06-030 | 17th January 2006
Piotr Berman, Jieun Jeong, Shiva Prasad Kasiviswanathan, Bhuvan Urgaonkar

Packing to angles and sectors

In our problem we are given a set of customers, their positions on the
plane and their demands. Geometrically, directional antenna with
parameters $\alpha,\rho,R$ is a set
of points with radial coordinates $(\theta,r)$ such that
$\alpha \le \theta \le \alpha+\rho$ and $r \le R$. Given a set of
possible directional ... more >>>

TR05-069 | 11th July 2005
Piotr Berman, Marek Karpinski

8/7-Approximation Algorithm for (1,2)-TSP

Revisions: 2

We design a polynomial time 8/7-approximation algorithm for the Traveling Salesman Problem in which all distances are either one or two. This improves over the best known approximation factor of 7/6 for that problem. As a direct application we get a 7/6-approximation algorithm for the Maximum Path Cover Problem, similarily ... more >>>

TR04-111 | 30th November 2004
Piotr Berman, Marek Karpinski, Alexander D. Scott, Alexander D. Scott

Computational Complexity of Some Restricted Instances of 3SAT

We prove results on the computational complexity of instances of 3SAT in which every variable occurs 3 or 4 times.

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TR04-049 | 15th June 2004
Piotr Berman, Marek Karpinski, Yakov Nekrich

Optimal Trade-Off for Merkle Tree Traversal

We prove upper and lower bounds for computing Merkle tree
traversals, and display optimal trade-offs between time
and space complexity of that problem.

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TR03-056 | 29th July 2003
Piotr Berman, Marek Karpinski

Approximability of Hypergraph Minimum Bisection

We prove that the problems of minimum bisection on k-uniform
hypergraphs are almost exactly as hard to approximate,
up to the factor k/3, as the problem of minimum bisection
on graphs. On a positive side, our argument gives also the
first approximation ... more >>>

TR03-049 | 25th June 2003
Piotr Berman, Marek Karpinski, Alexander D. Scott

Approximation Hardness of Short Symmetric Instances of MAX-3SAT

We prove approximation hardness of short symmetric instances
of MAX-3SAT in which each literal occurs exactly twice, and
each clause is exactly of size 3. We display also an explicit
approximation lower bound for that problem. The bound two on
the number ... more >>>

TR03-022 | 11th April 2003
Piotr Berman, Marek Karpinski, Alexander D. Scott

Approximation Hardness and Satisfiability of Bounded Occurrence Instances of SAT

We study approximation hardness and satisfiability of bounded
occurrence uniform instances of SAT. Among other things, we prove
the inapproximability for SAT instances in which every clause has
exactly 3 literals and each variable occurs exactly 4 times,
and display an explicit ... more >>>

TR03-008 | 11th February 2003
Piotr Berman, Marek Karpinski

Improved Approximation Lower Bounds on Small Occurrence Optimization

We improve a number of approximation lower bounds for
bounded occurrence optimization problems like MAX-2SAT,
E2-LIN-2, Maximum Independent Set and Maximum-3D-Matching.

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TR02-018 | 22nd March 2002
Piotr Berman, Marek Karpinski, Yakov Nekrich

Approximating Huffman Codes in Parallel

In this paper we present some new results on the approximate parallel
construction of Huffman codes. Our algorithm achieves linear work
and logarithmic time, provided that the initial set of elements
is sorted. This is the first parallel algorithm for that problem
with the optimal time and ... more >>>

TR01-097 | 11th December 2001
Piotr Berman, Marek Karpinski

Improved Approximations for General Minimum Cost Scheduling

We give improved trade-off results on approximating general
minimum cost scheduling problems.

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TR01-053 | 17th July 2001
Piotr Berman, Marek Karpinski

Efficient Amplifiers and Bounded Degree Optimization

This paper studies the existence of efficient (small size)
amplifiers for proving explicit inaproximability results for bounded degree
and bounded occurrence combinatorial optimization problems, and gives
an explicit construction for such amplifiers. We use this construction
also later to improve the currently best known approximation lower bounds
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TR01-047 | 3rd July 2001
Piotr Berman, Sridhar Hannenhalli, Marek Karpinski

1.375-Approximation Algorithm for Sorting by Reversals

Analysis of genomes evolving by inversions leads to a general
combinatorial problem of {\em Sorting by Reversals}, MIN-SBR, the problem of
sorting a permutation by a minimum number of reversals.
This combinatorial problem has a long history, and a number of other
motivations. It was studied in a great ... more >>>

TR01-026 | 3rd April 2001
Piotr Berman, Marek Karpinski

Approximation Hardness of Bounded Degree MIN-CSP and MIN-BISECTION

We consider bounded occurrence (degree) instances of a minimum
constraint satisfaction problem MIN-LIN2 and a MIN-BISECTION 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 ... more >>>

TR01-025 | 28th March 2001
Piotr Berman, Marek Karpinski

Approximating Minimum Unsatisfiability of Linear Equations

We consider the following optimization problem:
given a system of m linear equations in n variables over a certain field,
a feasible solution is any assignment of values to the variables, and the
minimized objective function is the number of equations that are not
satisfied. For ... more >>>

TR00-001 | 14th January 2000
Piotr Berman, Moses Charikar, Marek Karpinski

On-Line Load Balancing for Related Machines

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 $3+\sqrt{8}\approx 5.828$ for the deterministic
version, and $3.31/\ln 2.155 \approx 4.311$ for its randomized variant,
improving the previous competitive ratios ... more >>>

TR98-065 | 6th November 1998
Piotr Berman, Marek Karpinski

On Some Tighter Inapproximability Results, Further Improvements

Improved inaproximability results are given, including the
best up to date explicit approximation thresholds for bounded
occurence satisfiability problems, like MAX-2SAT and E2-LIN-2,
and problems in bounded degree graphs, like MIS, Node Cover
and MAX CUT. We prove also for the first time inapproximability
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TR98-029 | 27th May 1998
Piotr Berman, Marek Karpinski

On Some Tighter Inapproximability Results

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 first time inapproximability of the
problem of Sorting by ... more >>>

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