New models of graph-bin packing

نویسندگان

Csilla Bujtás

György Dósa

Csanád Imreh

Judit Nagy-György

Zsolt Tuza

چکیده

In [Int. J. Found. Computer Sci. 22 (2011) 1971–1993] the authors introduced a very general problem called Graph-Bin Packing (GBP). It requires a mapping μ : V (G) → V (H) from the vertex set of an input graph G into a fixed host graph H, which, among other conditions, satisfies that for each pair u, v of adjacent vertices the distance of μ(u) and μ(v) in H is between two prescribed bounds. In this paper we propose two online versions of the Graph-Bin packing problem. In both cases the vertices can arrive in an arbitrary order where each new vertex is adjacent to some of the previous ones. One version is a Maker-Breaker game whose rules are defined by the packing conditions. A subclass of Maker-win input graphs is what we call ‘well-packable’; it means that a packing of G is obtained whenever the mapping μ(u) is generated by selecting an arbitrary feasible vertex of the host graph for the next vertex of G in each step. The other model is connected-online packing where we are looking for an online algorithm which can always find a feasible packing. In both models we present some sufficient and some necessary conditions for packability. In the connected-online version we also give bounds on the size of used part of the host graph.

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