An On-Line Parallel Algorithm for Node Ranking of Trees
نویسندگان
چکیده
A node ranking of a graph G = (V,E) is a proper node coloring C : V → N such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) > C(x). In the on-line version of the node ranking problem, the nodes v1, v2, ..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2, ..., vi}] are known when the color for the node vi be chosen. And the assigned color can not be changed later. In this paper, we present a parallel algorithm to find an on-line node ranking for general tree. Our parallel algorithm needs O(n log n) time with using O(n/ log n) processors on CREW PRAM model.
منابع مشابه
Parallel Algorithm for On-Line Ranking in Trees
A node k-ranking of a graph G = (V, E) is a proper node coloring C: V {1, 2, ..., k} such that any x-y path in G with C(x) = C(y) contains an internal node z with C(z) C(x). In the on-line version of this problem, the nodes v1, v2,..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2,..., vi}] are known when the color of vi has to be chosen...
متن کاملParallel Generation of t-ary Trees
A parallel algorithm for generating t-ary tree sequences in reverse B-order is presented. The algorithm generates t-ary trees by 0-1 sequences, and each 0-1 sequences is generated in constant average time O(1). The algorithm is executed on a CREW SM SIMD model, and is adaptive and cost-optimal. Prior to the discussion of the parallel algorithm a new sequential generation with O(1) average time ...
متن کاملOn-line Ranking Algorithms for Trees
A node k-ranking of a graph G = (V, E) is a proper node coloring C: V {1, 2, ..., k} such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) C(x). In the on-line version of this problem, the nodes v1, v2,..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2, ..., vi}] are known when the color...
متن کاملA Hybrid Unconscious Search Algorithm for Mixed-model Assembly Line Balancing Problem with SDST, Parallel Workstation and Learning Effect
Due to the variety of products, simultaneous production of different models has an important role in production systems. Moreover, considering the realistic constraints in designing production lines attracted a lot of attentions in recent researches. Since the assembly line balancing problem is NP-hard, efficient methods are needed to solve this kind of problems. In this study, a new hybrid met...
متن کاملParallel Enumeration of t–ary Trees in ASC SIMD Model
In this paper parallel algorithms are presented for enumeration and unranking of t–ary trees with n internal nodes. Generation algorithms are designed in the associative computing model ASC that belongs to a broad category of SIMD models. Tree sequences are generated in lexicographical order, with O(1) time per object, in a new representation, as combinations with repetitions with restricted gr...
متن کامل