Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Regular Article: On the Complexity of DNA Physical Mapping
Advances in Applied Mathematics
Journal of the ACM (JACM)
The homogeneous set sandwich problem
Information Processing Letters
An efficient algorithm for solving the homogeneous set sandwich problem
Information Processing Letters
The graph sandwich problem for 1-join composition is NP-complete
Discrete Applied Mathematics
A note on finding all homogeneous set sandwiches
Information Processing Letters
Algorithms for the Homogeneous Set Sandwich Problem
Algorithmica
Theoretical Computer Science
Clustering with Partial Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Note on the Homogeneous Set Sandwich Problem
Information Processing Letters
The Pair Completion algorithm for the Homogeneous Set Sandwich Problem
Information Processing Letters
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Graph sandwich problems were introduced by Golumbic et al. (1994) in [12] for DNA physical mapping problems and can be described as follows. Given a property @P of graphs and two disjoint sets of edges E"1, E"2 with E"1@?E"2 on a vertex set V, the problem is to find a graph G on V with edge set E"s having property @P and such that E"1@?E"s@?E"2. In this paper, we exhibit a quasi-linear reduction between the problem of finding an independent set of size k=2 in a graph and the problem of finding a sandwich homogeneous set of the same size k. Using this reduction, we prove that a number of natural (decision and counting) problems related to sandwich homogeneous sets are hard in general. We then exploit a little further the reduction and show that finding efficient algorithms to compute small sandwich homogeneous sets would imply substantial improvement for computing triangles in graphs.