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By Sumit Ganguly, Ramesh Krishnamurti

This booklet collects the refereed lawsuits of the 1st overseas 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 in addition to 2 invited talks provided on the convention. The workshop coated a various variety of issues on algorithms and discrete arithmetic, together with computational geometry, algorithms together with approximation algorithms, graph idea and computational complexity.

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Thus, = lk +3k−1 as k > lk . bS (u) ≤ k + lk − 1 = k + 2lk2−2 < k + 2lk2−1 < k + lk +k−1 2 2 lk +3k−1 Thus, for both cases, we get bS (u) ≤ . 5 as lk ≥ 2. Conclusion and Future Work In this paper we considered a simple graph where cycles intersect at single vertex, namely k-cycle graph. As it turned out finding the exact broadcast time in this graph is not very simple. We give an approximation algorithm for the k-cycle graph, with the approximation ratio 2. We also show that our algorithm generates the optimum broadcast time when the difference of cycle lengths between each pair is at least 4.

The last possibility is that at least one path of Yη internally-intersects a path of Yρ and each not-empty intersection between a path of Yη and a path of Yρ contains at least one endpoint. Then, remove from each path in Yη the internal nodes of the intersection with each path in Yρ (notice that a path of Yη at most internally-intersects one path in Yρ ). In this case the number of new extremal 4 Such modification can be found in the full version of the paper. A PTAS for the Metric Case of the Minimum SROCT 19 points will be at most |Yη | and the set Y defined by the union of Yρ with the modified Yη is a set of internally-disjoint δ-ηρ-paths that satisfies ∪P ∈Y P = S and: 2 6 6 − 11 |ext(Y )| ≤ 3 +1 .

Ck but not in set X0 . 3 X2 : It consists of the cycles which has been informed from u along both directions. Let there are p such cycles and m + r + p = k. 4. 1. 1. 2. If l10 ≥ l11 − 1 u broadcasts along C10 at time i + 1. 3. Else-If l10 < l11 − 1 u broadcasts along C11 at time i + 1. 2. Else-If there is no cycle in X1 u broadcasts along C10 at time i + 1. 3. If u informs C10 update X1 = X1 + {C10 } and X0 = X0 − {C10 }. 4. Else-If u informs C11 update X2 = X2 + {C11 } and X1 = X1 − {C11 }. 5.

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