TY - GEN
T1 - DISTRIBUTIVE GRAPH ALGORITHMS-GLOBAL SOLUTIONS FROM LOCAL DATA.
AU - Linial, Nathan
PY - 1987
Y1 - 1987
N2 - Processors that reside in the vertices of a graph G and communicate only with their neighbors are considered. The system is synchronous and reliable, there is not limit on message lengths, and local computation is instantaneous. It is shown that a maximal independent set in an n-cycle cannot be found faster than OMEGA (log***n), and this is optimal. The d-regular tree of radius r cannot be colored with fewer than ROOT d colors in time 2r/3. If DELTA is the largest degree in G which has order n, then in time O(log*n) it can be colored with O( DELTA **2) colors.
AB - Processors that reside in the vertices of a graph G and communicate only with their neighbors are considered. The system is synchronous and reliable, there is not limit on message lengths, and local computation is instantaneous. It is shown that a maximal independent set in an n-cycle cannot be found faster than OMEGA (log***n), and this is optimal. The d-regular tree of radius r cannot be colored with fewer than ROOT d colors in time 2r/3. If DELTA is the largest degree in G which has order n, then in time O(log*n) it can be colored with O( DELTA **2) colors.
UR - http://www.scopus.com/inward/record.url?scp=0023589501&partnerID=8YFLogxK
U2 - 10.1109/sfcs.1987.20
DO - 10.1109/sfcs.1987.20
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AN - SCOPUS:0023589501
SN - 0818608072
SN - 9780818608070
T3 - Annual Symposium on Foundations of Computer Science (Proceedings)
SP - 331
EP - 335
BT - Annual Symposium on Foundations of Computer Science (Proceedings)
PB - IEEE
ER -