Algorithms and Discrete Applied Mathematics: First by Sumit Ganguly, Ramesh Krishnamurti

By Sumit Ganguly, Ramesh Krishnamurti

This ebook collects the refereed lawsuits of the 1st foreign convention onon Algorithms and Discrete utilized arithmetic, CALDAM 2015, held in Kanpur, India, in February 2015. the amount comprises 26 complete revised papers from fifty eight submissions besides 2 invited talks provided on the convention. The workshop coated a various diversity of subject matters on algorithms and discrete arithmetic, together with computational geometry, algorithms together with approximation algorithms, graph conception and computational complexity.

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Extra resources for Algorithms and Discrete Applied Mathematics: First International Conference, CALDAM 2015, Kanpur, India, February 8-10, 2015. Proceedings

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Ii) b(w) ≥ d + j 2 (iii) b(w) ≥ d + 2k+lj +2j−2 4 for any j, 1 ≤ j ≤ k. Proof. (i): By Lemma 3 there is a minimum time broadcast scheme from originator w in Gk in which w first sends the information along the shorter path towards vertex u. Considering this minimum broadcast scheme, u is informed no earlier than d time units. It takes another k − 1 time units to inform at least one vertex in each of the remaining k − 1 cycles from u. Recall that lj ≥ 2 for any j, where 1 ≤ j ≤ k. So, at least one more time unit is required to inform the second vertex on the cycle which initially receives the message from u at time unit d + k − 1.

Since starting at time d + tj onwards, Cj receives the message from both directions, then bS (w) ≤ d + tj − 1 + lj −tj +2j−1 2 = 2d+lj +tj +2j−3 2 2d+lj +2k+2j−3 as tj ≤ 2k − 1. From Lemma 2 2d+lj +2k+2j−3 2 4d+lj +2j+2k−2 = 2 − 4d+lj 4d+2 +2j+2k−2 < 2. ≤ 4(iii), we 2d+lj +2k+2j−4 2 S (w) can write bb(w) ≤ ≤ The above algorithm S is a (2 − )-approximation algorithm in general, but it generates the exact broadcast time for some subclasses of k-cycle graph. 4 Optimality of Approximation Algorithm S for Some Subclasses of Gk In this section we consider several cases depending on the length of Cj and for some cases we will present an optimal algorithm.

In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2003), pp. 76–85 (2003) 6. : Approximation algorithms for broadcasting and gossiping. J. Parallel and Distrib. Comput. 43(1), 47–55 (1997) 7. : Heuristic algorithms for personalized communication problems in point-to-point networks. In: Proceedings of the 4th Colloquium on Structural Information Communication Complexity (SIROCCO 1997), pp. 240–252 (1997) 8. : Comparison of heuristics for one-to-all and all-to-all communication in partial meshes.

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