On-line analysis of the TCP acknowledgment delay problem
Journal of the ACM (JACM)
Control Message Aggregation in Group Communication Protocols
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
A constant approximation algorithm for the one-warehouse multi-retailer problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Online make-to-order joint replenishment model: primal dual competitive algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithm for the one-warehouse multi-retailer problem
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Computational complexity of uncapacitated multi-echelon production planning problems
Operations Research Letters
ACM SIGACT News
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In the Control Message Aggregation (CMA) problem, control packets are generated over time at the nodes of a tree T and need to be transmitted to the root of T. To optimize the overall cost, these transmissions can be delayed and different packets can be aggregated, that is a single transmission can include all packets from a subtree rooted at the root of T. The cost of this transmission is then equal to the total edge length of this subtree, independently of the number of packets that are sent. A sequence of transmissions that transmits all packets is called a schedule. The objective is to compute a schedule with minimum cost, where the cost of a schedule is the sum of all the transmission costs and delay costs of all packets. The problem is known to be $\mathbb{NP}$-hard, even for trees of depth 2. In the online scenario, it is an open problem whether a constant-competitive algorithm exists. We address the special case of the problem when T is a chain network. For the online case, we present a 5-competitive algorithm and give a lower bound of 2+φ≈3.618, improving the previous bounds of 8 and 2, respectively. Furthermore, for the offline version, we give a polynomial-time algorithm that computes the optimum solution.