The optimality of distributive constructions of minimum weight and degree restricted spanning trees in a complete network of processors

Journal Article · Wed Apr 01 04:00:00 EST 1987 · SIAM J. Comput.; (United States)

DOI:https://doi.org/10.1137/0216019· OSTI ID:6442361

Korach, E; Moran, S; Zaks, S

In a previous paper the authors showed that the distributive construction of a spanning tree in a complete network of processors can be done in O(n log n) messages. They show in this work that if the spanning tree is required to satisfy certain properties, then the complexity of its construction increases: First they show that the construction of a minimum weight spanning tree requires, in the worst case, at least ..cap omega..(n/sup 2/) messages, and then they show that the construction of a spanning tree where the maximum degree is at most k may require at least ..cap omega..(n/sup 2//k) messages in the worst case. Actually, in both case the lower bounds are shown for the number of edges used in the worst case. Moreover, the results are valid for both asynchronous and synchronous networks, and are independent of the lengths of the messages. On the other hand, there are algorithms for the above tasks which achieve these lower bounds, up to a constant factor, and use messages of O(log n) length.

• Research Organization: Computer Science Dept., Technion-Israel Institute of Technology, Haifa
• OSTI ID: 6442361
• Journal Information: SIAM J. Comput.; (United States), Journal Name: SIAM J. Comput.; (United States) Vol. 16:2; ISSN SMJCA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
ARRAY PROCESSORS
COMMUNICATIONS
DATA PROCESSING
DATA TRANSMISSION
EQUIPMENT INTERFACES
MATHEMATICAL LOGIC
OPTIMIZATION
PROCESSING
TASK SCHEDULING