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We give deterministic distributed algorithms that given δ > 0 find in a planar graph G, (1 ± δ)-approximations of a maximum independent set, a maximum matching, and a minimum dominating set. The algorithms run in O(log∗ |G|) rounds. In addition, we prove that no faster deterministic approximation is possible and show that if randomization is allowed it is… (More)

- Michal Hanckowiak, Michal Karonski, Alessandro Panconesi
- SIAM J. Discrete Math.
- 1998

One of the fascinating questions of computer science is whether and to what extent randomization increases the power of algorithmic procedures. It is well-known that, in general, randomization makes distributed algorithms more powerful, for there are examples of basic coordination tasks in asynchronous systems which cannot be solved by deterministic… (More)

We give an efficient distributed algorithm that finds an almost optimal packing of a graph <i>H</i> in a planar graph <i>G</i>. The algorithm is deterministic and its running time is poly-logarithmic in the order of <i>G</i>.

- Andrzej Czygrinow, Michal Hanckowiak
- COCOON
- 2007

We give efficient distributed approximation algorithms for weighted versions of the maximum matching problem and the minimum dominating set problem for graphs from minor-closed families. To complement these results we indicate that no efficient distributed algorithm for the minimum weight connected dominating set exists.

- Andrzej Czygrinow, Michal Hanckowiak
- DISC
- 2007

We show that maximal matchings can be computed deterministically in O(log4 n) rounds in the synchronous, message-passing model of computation. This improves on an earlier result by three log-factors.

- Andrzej Czygrinow, Michal Hanckowiak, Edyta Szymanska
- Discrete Applied Mathematics
- 2004

We present a distributed algorithm that finds a matching M of size which is at least 2/3|M | where M ∗ is a maximum matching in a graph. The algorithm runs in O(log n) steps.

We present a distributed approximation algorithm that computes in every graph G a matching M of size at least 2 3 β(G), where β(G) is the size of a maximum matching in G. The algorithm runs in O(log |V (G)|) rounds in the synchronous, message passing model of computation and matches the best known asymptotic complexity for computing a maximal matching in… (More)