TY - GEN

T1 - Improved algorithms for polynomial-time decay and time-decay with additive error

AU - Kopelowitz, Tsvi

AU - Porat, Ely

PY - 2005

Y1 - 2005

N2 - We consider the problem of maintaining polynomial and exponential decay aggregates of a data stream, where the weight of values seen from the stream diminishes as time elapses. This type of aggregation was first introduced by Cohen and Strauss in [4]. These types of decay functions on streams are used in many applications in which the relative value of streaming data decreases since the time the data was seen. Some recent work and space efficient algorithms were developed for time-decaying aggregations, and in particular polynomial and exponential decaying aggregations. All of the work done so far has maintained multiplicative approximations for the aggregates. In this paper we present the first O(log N) space algorithm for the polynomial decay under a multiplicative approximation, matching a lower bound. In addition, we explore and develop algorithms and lower bounds for approximations allowing an additive error in addition to the multiplicative error. We show that in some cases, allowing an additive error can decrease the amount of space required, while in other cases we cannot do any better than a solution without additive error.

AB - We consider the problem of maintaining polynomial and exponential decay aggregates of a data stream, where the weight of values seen from the stream diminishes as time elapses. This type of aggregation was first introduced by Cohen and Strauss in [4]. These types of decay functions on streams are used in many applications in which the relative value of streaming data decreases since the time the data was seen. Some recent work and space efficient algorithms were developed for time-decaying aggregations, and in particular polynomial and exponential decaying aggregations. All of the work done so far has maintained multiplicative approximations for the aggregates. In this paper we present the first O(log N) space algorithm for the polynomial decay under a multiplicative approximation, matching a lower bound. In addition, we explore and develop algorithms and lower bounds for approximations allowing an additive error in addition to the multiplicative error. We show that in some cases, allowing an additive error can decrease the amount of space required, while in other cases we cannot do any better than a solution without additive error.

UR - http://www.scopus.com/inward/record.url?scp=33646173418&partnerID=8YFLogxK

U2 - 10.1007/11560586_25

DO - 10.1007/11560586_25

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AN - SCOPUS:33646173418

SN - 3540291067

SN - 9783540291060

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 309

EP - 322

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 9th Italian Conference on Theoretical Computer Science, ICTCS 2005

Y2 - 12 October 2005 through 14 October 2005

ER -