Research Interests:
Research Interests:
In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for... more
In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for the restricted version of the problem with improved performance guarantees. In this thesis, we investigate the approximation complexity of selected NP-hard optimization problems restricted to instances with bounded degree, occurrence or weight parameter. Specifically, we consider the family of dense instances, where typically the average degree is bounded from below by some function of the size of the instance. Complementarily, we examine the family of sparse instances, in which the average degree is bounded from above by some fixed constant. We focus on developing new methods for proving explicit approximation hardness results for general as well as for restricted instances. The fist part of the thesis contributes to the systematic investigation of ...
Research Interests:
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In... more
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In particular, we prove the best known lower bound for TSP with bounded metrics for the metric bound equal to 4.
Research Interests:
We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ǫ-dense and average ǭ-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum... more
We study the approximation complexity of the Minimum Edge Dominating Set problem in everywhere ǫ-dense and average ǭ-dense graphs. More precisely, we consider the computational complexity of approximating a generalization of the Minimum Edge Dominating Set problem, the so called Minimum Subset Edge Dominating Set problem. As a direct result, we obtain for the special case of the Minimum Edge Dominating Set problem in everywhere ǫ-dense and average ǭdense graphs by using the techniques of Karpinski and Zelikovsky, the approximation ratios of min{2, 3 1+2ǫ} and of min{2, 3 3−2 √ 1−ǭ}, respectively. On the other hand, we give new approximation lower bounds for the Minimum Edge Dominating Set problem in dense graphs. Assuming the Unique Game Conjecture, we show that it is NP-hard to approximate the Minimum Edge Dominating Set problem in everywhere ǫ-dense graphs with a ratio better than 2 1+ǫ with ǫ ≥ 1/2 and 2 2− √ 1−ǭ with ǭ ≥ 3/4 in average ǭ-dense graphs. Dept. of Computer Science, ...
We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.
Research Interests:
We study the approximation hardness of the Shortest Superstring, the Maximal Compression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem. We introduce a new reduction method that produces strongly restricted instances... more
We study the approximation hardness of the Shortest Superstring, the Maximal Compression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem. We introduce a new reduction method that produces strongly restricted instances of the Shortest Superstring problem, in which the maximal orbit size is eight (with no character appearing more than eight times) and all given strings having length four. Based on this reduction method, we are able to improve the best up to now known approximation lower bound for the Shortest Superstring problem and the Maximal Compression problem by an order of magnitude. The results imply also an improved approximation lower bound for the MAX-ATSP problem.
We present a new method for proving explicit approximation lower bounds for the Shortest Superstring problem, the Maximum Compression problem, Maximum Asymmetric TSP problem, the (1, 2)–ATSP problem, the (1, 2)–TSP problem, the (1,... more
We present a new method for proving explicit approximation lower bounds for the Shortest Superstring problem, the Maximum Compression problem, Maximum Asymmetric TSP problem, the (1, 2)–ATSP problem, the (1, 2)–TSP problem, the (1, 4)–ATSP problem and the (1, 4)–TSP problem improving on the best up to now known approximation lower bounds for those problems.
Research Interests:
We study approximation complexity of the Vertex Cover problem restricted to dense and subdense balanced k-partite k-uniform hypergraphs. The best known approximation algorithm for the general k-partite case achieves an approximation ratio... more
We study approximation complexity of the Vertex Cover problem restricted to dense and subdense balanced k-partite k-uniform hypergraphs. The best known approximation algorithm for the general k-partite case achieves an approximation ratio of k2 which is the best possible assuming the Unique Game Conjecture. In this paper, we present approximation algorithms for the dense and the subdense nearly regular instances both with an approximation factor strictly better than k2 . On the other hand, we show that the latter approximation upper bound is almost tight under the Unique Games Conjecture.
We develop a new method for proving explicit approximation lower bounds for the Shortest Superstring problem, the Maximum Compression problem, the Maximum Asymmetric TSP problem, the (1, 2)--ATSP problem and the (1, 2)--TSP problem... more
We develop a new method for proving explicit approximation lower bounds for the Shortest Superstring problem, the Maximum Compression problem, the Maximum Asymmetric TSP problem, the (1, 2)--ATSP problem and the (1, 2)--TSP problem improving on the best known approximation lower bounds for those problems.
Research Interests:
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In... more
We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In particular, we prove the best known lower bound for TSP with bounded metrics for the metric bound equal to 4.
Research Interests:
We study the approximation hardness of the Shortest Superstring, the Maximal Compression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem. We introduce a new reduction method that produces strongly restricted instances... more
We study the approximation hardness of the Shortest Superstring, the Maximal Compression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem. We introduce a new reduction method that produces strongly restricted instances of the Shortest Superstring problem, in which the maximal orbit size is eight (with no character appearing more than eight times) and all given strings having length four. Based on this reduction method, we are able to improve the best up to now known approximation lower bound for the Shortest Superstring problem and the Maximal Compression problem by an order of magnitude. The results imply also an improved approximation lower bound for the MAX-ATSP problem.
Research Interests:
... partition dimen-sions of a graph. Ars Combinatoria 88, 349366 (2008) 6. Chartrand, G., Eroh, L., Johnson, M., Oellermann, O.: Resolvability in graphs and the metric dimension of a graph. Disc. Appl. Math. 105, 99133 (2000) 7 ...