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A robot has to visit all nodes and traverse all edges of an unknown undirected connected graph, using as few edge traversals as possible. The quality of an exploration algorithm A is measured by comparing its cost (number of edge traversals) to that of the optimal algorithm having full knowledge of the graph. The ratio between these costs, maximized over… (More)

We consider the following clustering problems: given a general undirected graph, partition its vertices into disjoint clusters such that each cluster forms a clique and the number of edges within the clusters is maximized (Max-ECP), or the number of edges between clusters is minimized (Min-ECP). These problems arise naturally in the DNA clone… (More)

We consider deterministic broadcasting in <i>geometric radio networks</i> (GRN) whose nodes know only a limited part of the network Nodes of a GRN are situated in the plane and each of them is equipped with a transmitter of some range <i>r</i>. A signal from this node can reach all nodes at distance at most <i>r</i> from it but if a node is situated within… (More)

We present a randomized NC solution to the problem of constructing a maximum (cardinality) f-matching. As a corollary, we obtain a randomized NC algorithm for the problem of constructing a graph satisfying a sequence d 1 ; d 2 ;...; d n of equality degree constraints. We provide an optimal NC algorithm for the decision version of the degree sequence problem… (More)