arXiv subjects

Nicolas Nisse

Publications and source records attributed to Nicolas Nisse.

20 records · Page 2Linked to original sources

arXiv2010

Adding a referee to an interconnection network: What can(not) be computed in one round

In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model and it is close to the simultaneous messages (communication complexity) model defined by Babai, Kimmel and Lokam. More precisely, each of these n nodes -which only knows its own ID and the IDs of its neighbors- is allowed to send a message of O(log n) bits to some central entity, called the referee. Is it possible for the referee to decide some basic structural properties of the network topology G? We show that simple questions like, "does G contain a square?", "does G contain a triangle?" or "Is the diameter of G at most 3? cannot be solved in general. On the other hand, the referee can decode the messages in order to have full knowledge of G when G belongs to many graph classes such as planar graphs, bounded treewidth graphs and, more generally, bounded degeneracy graphs. We leave open questions related to the connectivity of arbitrary graphs.

cs.CC↗

arXiv2010

Cop and robber games when the robber can hide and ride

In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G. The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) and Quilliot (1983) characterized the cop-win graphs as graphs admitting a dismantling scheme. In this paper, we characterize in a similar way the class CW(s,s') of cop-win graphs in the game in which the cop and the robber move at different speeds s' and s, s'<= s. We also establish some connections between cop-win graphs for this game with s' =3, coincide and we provide a structural characterization of these graphs. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs in the game in which the robber is visible only every k moves for a fixed integer k>1. We characterize the graphs which are cop-win for any value of k. Finally, we consider the game where the cop wins if he is at distance at most 1 from the robber and we characterize via a specific dismantling scheme the bipartite graphs where a single cop wins in this game.

cs.DM↗