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We show that PSGs cannot be reduced to security games studied so far and we highlight their generality in tackling adversarial patrolling on arbitrary graphs.
Our results include improved analysis of two existing dimension-exchange algorithms for token distribution on arbitrary graphs and on arbitrary trees, respectively.
This code is capable of constructing and diagonalising the observables for spin 12 and spinless fermionic particles with many body interactions on arbitrary graphs using massively parallel distributed memory machines.
In this paper we present a new randomized algorithm and implementation with superior performance that for the first time achieves parallel speedup on arbitrary graphs (both regular and irregular topologies) when compared with the best sequential implementation for finding a spanning tree.
When divisible loads originate from a single node, we compare the proposed algorithm with a recently proposed RAOLD algorithm which is based on minimum cost spanning tree [J. Yao, V. Bharadwaj, Design and performance analysis of divisible load scheduling strategies on arbitrary graphs, Cluster Computing 7(20042004) 191 207].
Our aim here is somewhat broader, namely to establish general, formal relations between complexity measures defined on arbitrary graphs.
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Algorithms for automated classification tend not to perform efficiently when executed on arbitrary graph-based data structures, so a usual technique is to reduce graphs to characteristic features or descriptors, which serve as the input for classifiers.
The generalization from Leavitt path algebras of row-finite graphs to those of arbitrary graphs was achieved in two stages.
The greater topological complexity of arbitrary graph embeddings and meshes on higher genus surfaces can result in scaffolding strand routes that are knotted in 3 space, so we also present necessary caveats for these settings.
This result implies the first explicit lower bound on the approximability of the general version (i.e., for arbitrary graphs) of the problem.
Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions.
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