Simpler Sequential and Parallel Biconnectivity Augmentation
نویسندگان
چکیده
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph G with vertex connectivity k (k ≥ 1), the connectivity augmentation refers to a set S of edges whose augmentation toG increases its vertex connectivity by one. A minimum connectivity augmentation of G is the one in which S is minimum. In this paper, we focus our attention on connectivity augmentation of trees. Towards this end, we present a new sequential algorithm for biconnectivity augmentation in trees by simplifying the algorithm reported in [7]. The simplicity is achieved with the help of edge contraction tool. This tool helps us in getting a recursive subproblem preserving all connectivity information. Subsequently, we present a parallel algorithm to obtain a minimum connectivity augmentation set in trees. Our parallel algorithm essentially follows the overall structure of sequential algorithm. Our implementation is based on CREW PRAM model with O(∆) processors, where ∆ refers to the maximum degree of a tree. We also show that our parallel algorithm is optimal whose processor-time product is O(n) where n is the number of vertices of a tree, which is an improvement over the parallel algorithm reported in [3].
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ورودعنوان ژورنال:
- CoRR
دوره abs/1307.1772 شماره
صفحات -
تاریخ انتشار 2013