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Communication complexity of distributed computing and a parallel algorithm for polynomial roots

Thesis/Dissertation ·
OSTI ID:6677370
The first part of this thesis begins with a discussion of the minimum communication requirements in some distributed networks. The main result is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks. This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array. Applications of this technique yield nontrivial optimal or near-optimal lower bounds on the communication complexity of distinctness, ranking, uniqueness, merging, and triangle detection on a ring, a mesh, and a complete binary tree of processors. A technique similar to the one used in proving the above results, yields interesting graph theoretic results concerning decomposition of a graph into complete bipartite subgraphs. The second part of the this is devoted to the design of a fast parallel algorithm for determining all roots of a polynomial. Given a polynomial rho(z) of degree n with m bit integer coefficients and an integer ..mu.., the author considers the problem of determining all its roots with error less than 2/sup -..mu../. It is shown that this problem is in the class NC if rho(z) has all real roots.
Research Organization:
Illinois Univ., Urbana (USA)
OSTI ID:
6677370
Country of Publication:
United States
Language:
English