Inverting sets and the packing problem
- Los Alamos National Lab., NM (United States)
- Rensselaer Polytechnic Inst., Troy, NY (United States). Dept. of Computer Science
- Technical Univ. of Nova Scotia, (Canada). School of Computer Science
- Nebraska Univ., Omaha, NE (United States). Dept. of Mathematics and Computer Science
Given a set V, a subset S, and a permutation {pi} of V, we say that {pi} permutes S if {pi}(S) {intersection} S = {theta}. Given a collection S = (V; S{sub 1}..., S{sub m}), where S{sub i} {improper_subset} V (i = 1,...,m), we say that S is invertible if there is a permutation {pi} of V such that {pi}(S{sub i}) {improper_subset} V -- S{sub i}. In this paper, we present necessary and sufficient conditions for the invertibility of a collection and construct a polynomial algorithm which determines whether a given collection is invertible. For an arbitrary collection, we give a lower bound for the maximum number of sets that can be inverted. Finally, we consider the problem of constructing a collection of sets such that no sub-collection of size three is invertible. Our constructions of such collections come from solutions to the packing problem with unbounded block sizes. We prove several new lower and upper bounds for the packing problem and present a new explicit construction of packing.
- Research Organization:
- Los Alamos National Lab., NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 10112033
- Report Number(s):
- LA-UR-92-3725; CONF-9206317-1; ON: DE93003822; CNN: Grant MDA-904-90-H-4027; Grant IRI-8900511; Grant CDA-8805910; Grant CCR-8810609
- Resource Relation:
- Conference: 7. international conference on graph theory, combinatorics, algorithms, and applications,Kalamazoo, MI (United States),1-5 Jun 1992; Other Information: PBD: [1992]
- Country of Publication:
- United States
- Language:
- English
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