Geodesic
Block allocation of a sequential resource
Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 79-88.

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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.
DOI : 10.26493/1855-3974.1508.f8c
Keywords: Maximal matching, maximal packing 
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Tomislav Došlić. Block allocation of a sequential resource. Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 79-88. doi : 10.26493/1855-3974.1508.f8c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1508.f8c/

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