Abstract
We present here techniques which exhibit optimal processor-time tradeoff for many important problems on sparse graphs. These problems include: maximal coloring and maximal independent set in trees and bounded degree graphs; 7-colorability, maximal independent set and maximal matching in planar graphs; maximum independent set, maximum matching and Hamiltonian path on rectangular grid graphs. Our techniques are based on the general list ranking problem: given k lists having a total of n elements, find for each element the membership relation and the rank of the element in its list. We solve this problem in O(log n) time with n/log n processors on an EREW PRAM. For trees and bounded degree graphs our methods need O(log n) time and n/log n processors on an EREW PRAM. For planar graphs they need O(log2 n) time and n/log2 n processors on an EREW PRAM using linear space. For the case of rectangular grid graphs they need O(log n) time with n/log n processors on a CRCW PRAM, or on an EREW PRAM (if the embedding is given).
This work was partially supported by the EEC ESPRIT Basic Research Action No. 3075 (ALCOM) and by the Ministry of Industry, Energy and Technology of Greece.
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© 1991 Springer-Verlag Berlin Heidelberg
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Pantziou, G.E., Spirakis, P.G., Zaroliagis, C.D. (1991). Optimal parallel algorithms for sparse graphs. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1990. Lecture Notes in Computer Science, vol 484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53832-1_27
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DOI: https://doi.org/10.1007/3-540-53832-1_27
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