Amortized efficiency of list update and paging rules
Communications of the ACM
TCP dynamic acknowledgment delay (extended abstract): theory and practice
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
A guessing game and randomized online algorithms
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
On-line analysis of the TCP acknowledgment delay problem
Journal of the ACM (JACM)
Dynamic TCP acknowledgement and other stories about e/(e-1)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A faster off-line algorithm for the TCP acknowledgement problem
Information Processing Letters
Competitive Analysis for the On-line Truck Transportation Problem
Journal of Global Optimization
Tight bounds for delay-sensitive aggregation
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Dynamic TCP acknowledgment with sliding window
Theoretical Computer Science
Optimally competitive list batching
Theoretical Computer Science
Online function tracking with generalized penalties
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Dynamic tcp acknowledgment with sliding window
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We study the problem of acknowledging a sequence of data packets that are sent across a TCP connection. Previous work on the problem has focused mostly on the objective function that minimizes the sum of the number of acknowledgements sent and the delays incurred for all of the packets. Dooly, Goldman and Scott presented a deterministic 2-competitive online algorithm and showed that this is the best competitiveness of a deterministic strategy. Recently Karlin, Kenyon and Randall developed a randomized online algorithm that achieves an optimal competitive ratio of e/(e -- 1) ≈ 1.58.In this paper we investigate a new objective function that minimizes the sum of the number of acknowledgements sent and the maximum delay incurred for any of the packets. This function is especially interesting if a TCP connection is used for interactive data transfer between network nodes. The TCP acknowledgement problem with this new objective function is different in structure than the problem with the function considered previously. We develop a deterministic online algorithm that achieves a competitive ratio of π2/6 , ≈ 1.644 and prove that no deterministic algorithm can have a smaller competitiveness. We also study a generalized objective function where delays are taken to the p-th power, for some positive integer p. Again we give tight upper and lower bounds on the best possible competitive ratio of deterministic online algorithms. The competitiveness is 1 plus an alternating sum of Riemann's zeta function and tends to 1.5 as p → ∞. Finally we consider randomized online algorithms and show that, for our first objective function, no randomized strategy can achieve a competitive ratio smaller than 3/(3 -- 2/e) ≈ 1.324. For the generalized objective function we show a lower bound of 2/(2 -- 1/e) ≈ 1.225.