Abstract
Online Algorithms for Hierarchical Aggregation Problems Data and inventory aggregation problems arise in multicasting, sensor networks, communication in organization hierarchies, and in supply chain management. These problems are naturally online, in the sense that aggregation decisions need to be made without information about future requests. We study these problems with a general tree structure of links that can be used for deliveries. This generalizes some well-studied optimization problems: trees of depth one capture the TCP acknowledgment problem, and trees of depth two capture the joint replenishment problem. For trees of depth one and two, constant-competitive online algorithms are known. We solve a major open problem by giving a constant-competitive algorithm for trees of arbitrary (fixed) depth. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines.
Highlights
Certain optimization problems can be formulated as aggregation problems
TCP Acknowledgment Problem (TCP-AP) is equivalent to the classical Lot Sizing Problem studied in the operations research literature since the 1950s. (See, for example, [30].) In the offline variant of TCP-AP, that is when all arrival times of control messages are known beforehand, an optimal schedule for aggregated packets can be computed with dynamic programming in time O(n log n) [1]
We mostly focus on the online version of Multi-Level Aggregation Problem (MLAP), where an algorithm needs to produce a schedule in response to requests that arrive over time
Summary
Certain optimization problems can be formulated as aggregation problems. They typically arise when expensive resources can be shared by multiple agents, who incur additional expenses for accessing a resource. Packet aggregation decisions must be done on the fly, without any information about future message releases This scenario is captured by the online variant of TCP-AP that has been well studied; it is known that the optimal competitive ratio is 2 in the deterministic case [15] and e/(e − 1) ≈ 1.582 in the randomized case [17, 11, 28]. The need to consider more tree-like (in a broad sense) supply hierarchies has been advocated in [20] These applications have inspired research on offline and online approximation algorithms for multi-level aggregation problems. Khanna et al [18] gave a rent-or-buy solution (that serves a group of requests once their waiting cost reaches the cost of their service) and showed that their algorithm is O(log α)-competitive, where α is defined as the sum of all edge weights. Depth 1 rand. alg. for depth 1 depth 2 fixed depth D ≥ 2 paths of arbitrary depth
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
