Block allocation of a sequential resource

Tomislav Došlić

Abstract


An H-packing of G is a collection of vertex-disjoint subgraphs of G such that each component is isomorphic to H. An H-packing of G is maximal if it cannot be extended to a larger H-packing of G. In this paper we consider problem of random allocation of a sequential resource into blocks of m consecutive units and show how it can be successfully modeled in terms of maximal Pm-packings. We enumerate maximal Pm-packings of Pn of a given cardinality and determine the asymptotic behavior of the enumerating sequences. We also compute the expected size of m-packings and provide a lower bound on the efficiency of block-allocation.


Keywords


Maximal matching, maximal packing

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DOI: https://doi.org/10.26493/1855-3974.1508.f8c

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications