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A robot with <i>k</i>-bit memory has to explore a tree whose nodes are unlabeled and edge ports are locally labeled at each node. The robot has no <i>a priori</i> knowledge of the topology of the tree or of its size, and its aim is to traverse all the edges. While <i>O</i>(log&#916;) bits of memory suffice to explore any tree of maximum degree &#916; if(More)
Let k be a positive integer, a subset Q of the set of vertices of a graph G is k-dependent in G if each vertex of Q has no more than k neighbours in Q. We present a parallel algorithm which computes a maximal k-dependent set in a graph on n nodes in time O(log 4 n) on an EREW PRAM with O(n 2) processors. In this way, we establish the membership of the(More)
We consider the problem of distributed deterministic broadcasting in radio networks. Nodes send messages in synchronous time-slots. Each node v has a given transmission range. All nodes located within this range can receive messages from v. However, a node situated in the range of two or more nodes that send messages simultaneously, cannot receive these(More)