A. NATANZON, R. SHAMIR, AND R. SHARAN, A polynomial approximation algorithm for the minimum fill-in problem, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC'98), New York, May 23--26 1998, ACM Press, pp. 41--47. Home/Search Document Details and Download
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Nested Graph Dissection and Approximation Algorithms - Guha (2000) (Correct)
....[38] is an excellent survey on uses of elimination trees. In [28, 39] the smallest height elimination tree was constructed for chordal graphs. All of the above problems are NP Hard. In [1, 30] the rst polynomial time approximation for these were proposed. This was improved and supplemented in [44]. In [1] it was shown that there exists an ordering which simultaneously approximates the three most known parameters, approximation results were also provided. In our work we improve both the existential and the approximability results. In [7] it was investigated if there exist better orderings ....
....with bounded degree d. In e ect, this is the rst o(n) approximation for the operation count problem, since we improve the dependence on the parameter d. We improve the approximation ratio of these quantities by factors of O(log n) and O(d 1 3 log 2 n) respectively. Combined with results in [44], this improves the best approximation ratio for the minimum ll in problem by a logarithmic factor. We present a di erent way of accounting for ll in and operation count than in [1, 30] which allows the improved results to be proved. We show that there exists a nested dissection ordering that ....
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A. Natanzon, R. Shamir, and R. Sharan. \A polynomial Approximation Algorithm for the Minimum Fill-In Problem". In Proceeding of Symposium on Theory of Computing (1998).
Complexity Classification of Some Edge Modification Problems - Natanzon, Shamir, Sharan (1999) (8 citations) Self-citation (Natanzon Shamir Sharan) (Correct)
....not include (pre defined) forbidden edges. Polynomial algorithms or NP hardness results are known for many sandwich problems [15, 18, 20, 23] Results on the parametric complexity of several completion problems were also obtained [8, 24] Approximation algorithms exist for several problems. In [31] an 8k approximation algorithm is given for the minimum fill in problem, where k denotes the size of an optimum solution. In [1] an O(m 1=4 log 3:5 n) approximation algorithm is given for the minimum chordal supergraph problem (where one wishes to minimize the total number of edges in the ....
A. NATANZON, R. SHAMIR, AND R. SHARAN, A polynomial approximation algorithm for the minimum fill-in problem, in Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC'98), New York, May 23--26 1998, ACM Press, pp. 41--47.
Perfect Completion and Deletion in Random Graphs - Natanzon, Shamir Self-citation (Natanzon Shamir) (Correct)
....Young [8] and deletion was shown to be NP complete by Yannakakis [16] Natanzon et al. [12] have shown the NP hardness of several edge modification problems including comparability editing, perfect editing, deletion and completion. Approximation algorithms exist for variants of chordal completion [1, 11] and interval completion [13] A natural combinatorial question arises when dealing with completion problems. How large can the completion set size be compared to the original graph size In this paper we study lower bounds for sizes of the modified edge sets with respect to perfect completion and ....
A. Natanzon, R. Shamir, and R. Sharan. A polynomial approximation algorithm for the minimum fillin problem. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC-98), pages 41--47, New York, May 23--26 1998. ACM Press.
Complexity Classification of Some Edge Modification Problems - Natanzon, Shamir, Sharan (1999) (8 citations) Self-citation (Natanzon Shamir Sharan) (Correct)
....not include (pre defined) forbidden edges. Polynomial algorithms or NP hardness results are known for many sandwich problems [16, 15, 18, 21] Several results on the parametric complexity of completion problems were also obtained [22, 7] Approximation algorithms exist for several problems. In [28] an 8k approximation algorithm is given for the minimum fill in problem, where k denotes the size of an optimum solution. In [1] an O(m 1=4 log 3:5 n) approximation algorithm is given for the minimum chordal supergraph problem (where one wishes to minimize the total number of edges in the ....
A. Natanzon, R. Shamir, and R. Sharan. A polynomial approximation algorithm for the minimum fill-in problem. In Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC'98), pages 41--47, New York, May 23--26 1998. ACM Press.
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