Abstract
We analyze the online call admission problem on grids, thus generalizing previous results for the path graph. Here the goal is to admit as many communication requests between pairs of computers in a given grid network as possible. The requests arrive in an online fashion, and ask to establish permanent edge-disjoint connections. We are particularly interested in examining how much information about future requests a central authority needs in order to compute an optimal solution or a solution of some given quality; we quantify this information by studying the advice complexity of the problem.Our results show that, without additional information, the central authority cannot perform satisfactorily well, and we establish a lower bound linear in |E| for the number of advice bits needed for near-optimal solutions, where |E| denotes the number of edges in the grid. Furthermore, concerning optimality, we are able to prove nearly tight bounds of at least 0.94|E| and at most 3|E| advice bits. In addition, we state another upper bound in the number of requests k and the number of vertices |V| in the grid of ⌈log25⋅k+log23⋅|V|⌉+⌈2log2k⌉ advice bits, which is stronger for a small number of requests.
Published Version
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