Complexity and algorithms for graph and hypergraph sandwich problems

Martin Charles Golumbic, Amir Wassermann

Research output: Contribution to journalArticlepeer-review


The script F sign Hypergraph Sandwich Problem (script F signHSP) is introduced here as follows: Given two hypergraphs H1 = (X, script E sign1) and H2 = (X, script E sign2) where script E sign1 = {E11, . . . , Em1}, script E sign2 = {E12, . . . , Em2} and Ei1 ⊆ Ei2 for all 1 ≤ i ≤ m, is there a hypergraph H = (X, script E sign) with script E sign = {E1, . . . , Em} such that Ei1 ⊆ Ei ⊆ Ei2 for all 1 ≤ i ≤ m which belongs to a specified hypergraph family script F sign? Hypergraph sandwich problems for several properties studied here occur in a variety of important applications. We prove the NP-completeness of the Interval HSP and the Circular-arc HSP. This corresponds to the problem of deciding whether a partially specified (0,1)-valued matrix can be filled in such that the resulting 0/1 matrix has the consecutive ones property, (resp., circular ones property). The consecutive ones property arises in databases and in DNA physical mapping. Further results shown are a set of conditions relating interval hypergraphs with acyclic hypergraphs. Finally, the k-tree graph sandwich problem is studied. The general problem is shown to be NP-complete and the fixed k version is given a polynomial algorithm. Both problems are based on solutions to the corresponding partial k-tree recognition problems.

Original languageEnglish
Pages (from-to)223-239
Number of pages17
JournalGraphs and Combinatorics
Issue number3
StatePublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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