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

M3 - Conference contribution

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 -