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By Sumit Ganguly, Ramesh Krishnamurti

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

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

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Approximation algorithms for minimum time broadcast. SIAM J. Discrete Math. 8, 401–427 (1995) 15. : Minimum broadcast time is np-complete for 3-regular planar graphs and deadline 2. Inf. Proc. Lett. 46, 281–287 (1993) 16. : Rapid rumor ramification: approximating the minimum broadcast time. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), pp. 202–213 (1994) 17. : Heuristic algorithms for broadcasting in point-to-point computer networks. IEEE Trans. Comput.

S. Alam and A. Mukhopadhyay s Z Y r2 q2 r1 Q B A q1 P r3 q3 p2 p1 X p3 Fig. 5. The 3-path graph Fig. 4. The jewel graph By Theorem 2, a 7-cycle has 42 different layer graph representations. We find conditions that make these impossible. By Theorem 1, these constitute the set of conditions for the line rigidity of the 7-cycle. The 42 layer graphs for a 7cycle form 6 groups, based on the number of edges on each side. For the 7-cycle (p1 , q1 , r1 , s, r2 , q2 , p2 ), Fig. 6 shows a representative layer graph for each group.

S. Alam and A. Mukhopadhyay Among the 42 rigidity conditions in Lemma 1 for the 7-cycle, 20 involve q1 r1 or q2 r2 . We next show how to replace these 20 conditions with ones sans these edges. To this end, for each of these conditions, first we try to use other edges of the cycle in the layer graph representation corresponding to that condition. If this fails, then we embed the layer graph representation, corresponding to that condition, into all possible layer graph representations of the entire G3p , and derive a rigidity condition from each such embedding.

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