TY - GEN

T1 - A time-randomness tradeoff for oblivious routing

AU - Krizanc, Danny

AU - Peleg, David

AU - Upfal, Eli

PY - 1988

Y1 - 1988

N2 - Three parameters characterize the performance of a probabilistic algorithm: T, the runtime of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps and R, the amount of randomness used by the algorithm, measured by the entropy of its random source. We present a tight tradeoff between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks. We prove a (1 - Q) log N/T - log Q - O(1) lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q. We show that this lower bound is almost optimal by proving the existence, for every e3 log N ≤ T ≤ N1/2 an oblivious algorithm that terminates in T steps with probability 1 - Q and uses (l-Q+o(1))log N/T-log Q, independent random bits. We complement this result with an explicit construction of a family of oblivious algorithms that use less than a factor of log N more random bits than the optimal algorithm achieving the same run-time.

AB - Three parameters characterize the performance of a probabilistic algorithm: T, the runtime of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps and R, the amount of randomness used by the algorithm, measured by the entropy of its random source. We present a tight tradeoff between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks. We prove a (1 - Q) log N/T - log Q - O(1) lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q. We show that this lower bound is almost optimal by proving the existence, for every e3 log N ≤ T ≤ N1/2 an oblivious algorithm that terminates in T steps with probability 1 - Q and uses (l-Q+o(1))log N/T-log Q, independent random bits. We complement this result with an explicit construction of a family of oblivious algorithms that use less than a factor of log N more random bits than the optimal algorithm achieving the same run-time.

UR - http://www.scopus.com/inward/record.url?scp=84894203891&partnerID=8YFLogxK

U2 - 10.1145/62212.62221

DO - 10.1145/62212.62221

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84894203891

SN - 0897912640

SN - 9780897912648

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 93

EP - 102

BT - Proceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC 1988

PB - Association for Computing Machinery

T2 - 20th Annual ACM Symposium on Theory of Computing, STOC 1988

Y2 - 2 May 1988 through 4 May 1988

ER -