An original parallel algorithm is presented that stems from a suitable physical metaphor by considering each edge of the graph as a cell that is attracted by the corresponding vertices and finally moves towards the one of them that wins the competition.

The linkage between economic activity and geography is obvious: Populations cluster mainly on coasts and rarely on ice sheets. Past studies of the relationships between economic activity and geography have been hampered by limited spatial data on economic activity. The present study introduces data on global economic activity, the G-Econ database, which measures economic activity for all large ...

Every 2-connected simple cubic graph of order n ≥ 6 has a cycle cover with at most dn4 e cycles. This bound is best possible.

A k-uniform, d-regular instance of Exact Cover is a family of m sets Fn,d,k = {Sj ⊆ {1, . . . , n}}, where each subset has size k and each 1 ≤ i ≤ n is contained in d of the Sj . It is satisfiable if there is a subset T ⊆ {1, . . . , n} such that |T ∩ Sj | = 1 for all j. Alternately, we can consider it a d-regular instance of Positive 1-in-k SAT, i.e., a Boolean formula with m clauses and n var...

A graph H is a cover of a graph G if there exists a mapping φ from V (H) onto V (G) such that for every vertex v of G, φ maps the neighbours of v in H bijectively onto the neighbours of φ(v) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. This conjecture is not completely solved yet, but partial results due to A...

In this paper, we consider the classical NP-complete VERTEX COVER problem in large graphs. We assume that the size and the access to the input graph impose the following constraints: (1) the input graph must not be modified (integrity of the input instance), (2) the computer running the algorithm has a memory of limited size (compared to the graph) and (3) the result must be sent to an output m...

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Central Research Unit The views expressed in this report are those of the researchers and do not necessarily represent those of the Department or Scottish Ministers. Further copies of this report are available priced £5.00. Cheques should be made payable to The Stationery Office Ltd and addressed to: ACKNOWLEDGEMENTS We would like to acknowledge the patience and time of the great many people, o...

[The data used in this paper were collected for the Australian Institute of Criminology’s Drug Use Monitoring in Australia project by the National Drug Research Institute at Curtin University of Technology, Marg Hauritz Pty Ltd and Forsythe Consultants Pty Ltd, with the assistance of the Queensland, New South Wales and Western Australian Police Services. Neither the collectors nor the police se...