In [1], whether a target binary string s can be represented from a boolean formula with operands chosen from a set of binary strings W was studied. In this paper, we first examine selecting a maximum subset X from W, so that for any string t in X, t is not representable by X\{t}. We rephrase this problem as graph, and surprisingly find it give rise to a broad model of edge packing problem, which itself falls into the model of forbidden subgraph problem. Specifically, given a graph G(V,E) and a constant c, the problem asks to choose as many as edges to form a subgraph G′. So that in G′, for each edge, at least one of its endpoints has degree no more than c. We call such G′ partial c degree bounded. This edge packing problem model also has a direct interpretation in resource allocation. There are n types of resources and m jobs. Each job needs two types of resources. A job can be accomplished if either one of its necessary resources is shared by no more than c other jobs. The problem then asks to finish as many jobs as possible. For edge packing problem, when c = 1, it turns out to be the complement of dominating set and able to be 2-approximated. When c = 2, it can be 32/11-approximated. We also prove it is NP-complete for any constant c on graphs and is O(|V| 2) solvable on trees. We believe this partial bounded graph problem is intrinsic and merits more attention. © 2012 Springer-Verlag.
CITATION STYLE
Zhang, P. (2012). Partial degree bounded edge packing problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7285 LNCS, pp. 359–367). https://doi.org/10.1007/978-3-642-29700-7_33
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