By Bob Stat
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On the power of additive combinatorial search model. In Proc. of Computing and Combinatorics, 4th Annual International Conference, COCOON’98, Taipei, Taiwan, August 12-14, 1998, volume 1449 of Lecture Notes in Computer Science, pages 194–203. Springer, 1998. 11. V. Grebinski and G. Kucherov. Reconstructing a hamiltonian cycle by querying the graph: Application to DNA physical mapping. Discrete Applied Mathematics, 88:147–165, 1998. 12. V. Grebinski and G. Kucherov. Reconstructing set partitions.
The approach is based on a fully dynamic modular decomposition algorithm for permutation graphs that works in O(n) time per edge and vertex modification. We thereby obtain a fully dynamic algorithm for the recognition of permutation graphs. g. ) for a family F of graphs aims to maintain a characteristic representation of dynamically changing graphs as long as the modiﬁed graph belongs to F . The input of the problem is a graph G ∈ F with its representation and a series of modiﬁcations. Any modiﬁcation is of the following: inserting or deleting a vertex (along with the edges incident to it), inserting or deleting an edge.
We show that under this model, nonadaptive algorithms get all their power and often allow to achieve (or to approach) the lower bound. This is due to powerful combinatorial constructions of (0, 1)-matrices verifying certain properties. 1 Hamiltonian Cycles We start again with our initial problem of reconstructing a Hamiltonian cycle on n vertices. As under the quantitative model there are n + 1 possible answers to each query Q ⊆ V , the information-theoretic lower bound is logn+1 (n−1)! = 2 (1 + o(1)) · n.