Online Balancing Two Independent Criteria upon Placements and Deletions

We study the online bicriteria load balancing problem in this paper. We choose a system of distributed homogeneous file servers located in a cluster as the scenario and propose an online approximate solution for balancing their loads and required storage spaces upon placements and deletions. By placement (resp. deletion), we mean to insert a document into (resp. remove a document from) a server system. The main technique is to keep two global quantities large enough. To the best of our knowledge, the technique is novel, and the result is the first one, in the literature. Our result works for any sequences of document placements and deletions. For each deletion, a limited number of documents are reallocated. The load and storage space bounds are 1.5 to 4 times those in the best existing result for sole placements. We refer sole placements to those placement algorithms that do not allow any reallocation and replication. The time complexity, for each operation, is O(logMN), where M is the number of servers, and N is the number of existing documents in the servers, plus the reallocation cost for document deletion. The price for handling document deletion is almost totally reflected by the reallocation cost, and the higher bounds of load and storage spaces, while the O(logN) additive term in the time complexity serves as the remainder.