Online Algorithms for Multilevel Aggregation

• 成果类型: Article
• 署名作者: Bienkowski, Marcin; Bohm, Martin; Byrka, Jaroslaw; Chrobak, Marek; Durr, Christoph; Folwarczn, Lukas; Jez, Lukasz; Sgall, Jiri; Nguyen Kim Thang; Vesely, Pavel
• 署名单位: University of Wroclaw; University of Bremen; Charles University Prague; University of California System; University of California Riverside; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Universite Paris Cite; Universite Paris Saclay; University of Warwick
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1847
• 发表日期: 2020
• 页码: 214-232
• 关键词: algorithmic aspects of networks; Online algorithms; scheduling and resource allocation; Iot sizing; multistage assembly problem

摘要

In the multilevel aggregation problem (MLAP), requests arrive at the nodes of an edge-weighted tree J and have to be served eventually. A service is defined as a subtree X of J that contains the root of J. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subbees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the Transmission Control Protocol acknowledgment problem, whereas for trees of depth 2, it is equivalent to the joint replenishment problem. Aggregation problems for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and supply chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant-competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant-competitive online algorithm for trees of arbitrary (fixed) depth. The competitive ratio is O(D(4)2(D)), where D is the depth of J. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines.