266 research outputs found
DMVP: Foremost Waypoint Coverage of Time-Varying Graphs
We consider the Dynamic Map Visitation Problem (DMVP), in which a team of
agents must visit a collection of critical locations as quickly as possible, in
an environment that may change rapidly and unpredictably during the agents'
navigation. We apply recent formulations of time-varying graphs (TVGs) to DMVP,
shedding new light on the computational hierarchy of TVG classes by analyzing them in the
context of graph navigation. We provide hardness results for all three classes,
and for several restricted topologies, we show a separation between the classes
by showing severe inapproximability in , limited approximability
in , and tractability in . We also give topologies in
which DMVP in is fixed parameter tractable, which may serve as a
first step toward fully characterizing the features that make DMVP difficult.Comment: 24 pages. Full version of paper from Proceedings of WG 2014, LNCS,
Springer-Verla
A Comparison of Meshes With Static Buses and Unidirectional Wrap-Arounds
We investigate the relative computational powers of a mesh with static buses and a mesh with unidirectional wrap-mounds. A mesh with unidirectional wraparounds is a torus with the restriction that any wraparoundlink of the architecture can only transmit data in one of the two directions at any clock tick. We show that the problem of packet routing can be solved as efficiently on a linear array with unidirectional wrap-around link as on a linear array with a broadcast bus. We also present a routing algorithm for a twcdimensional torus with unidirectional wraparound links whose run time is close to that of the best known algorithm for routing on a mesh with broadcast buses in each dimension. In addition, we show that on a mesh with broadcast buses, sorting can be done in time that is essentially the same as the time needed for packet routing
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