Improved Approximation Guarantees for Weighted Matching in the Semi-streaming Model

Abstract

We study the maximum weight matching problem in the semi-streaming model, and improve on the currently best one-pass algorithm due to Zelke (Proc. STACS '08, pages 669-680) by devising a deterministic approach whose performance guarantee is 4.91 + ε. In addition, we study preemptive online algorithms, a sub-class of one-pass algorithms where we are only allowed to maintain a feasible matching in memory at any point in time. All known results prior to Zelke's belong to this sub-class. We provide a lower bound of 4.967 on the competitive ratio of any such deterministic algorithm, and hence show that future improvements will have to store in memory a set of edges which is not necessarily a feasible matching.

Dynamic Graphs in the Sliding-Window Model

“…We combine our algorithm for maximum cardinality matching with the approach of Epstein et al [17] to give a 9.027 approximation. In this approach, we partition the set of edges into classes of geometrically increasing weights and construct a large cardinality matching in each weight class.…”

“…This includes both traditional data structures where the goal is to enable fast updates and queries [16,[22][23][24]29] and data stream algorithms where the primary goal is to design randomized data structures of sublinear size that can answer queries with high probability [2,3,17,18,25,27,30]. The paper focuses on the latter: specifically, processing graphs using sublinear space in the sliding-window model.…”

Streaming Algorithms for Independent Sets

“…A number of graph problems have been studied in the semi-streaming model, including bipartite matching (weighted and unweighted cases) [10,9], diameter and shortest paths [10,11], min-cut [1], and graph spanners [11]. The independent set (IS) problem, to our best knowledge, has not been studied in the model before.…”

“…This defines a new online streaming model. It is closely related to preemptive online algorithms, considered recently by Epstein et al [9] in a streaming context for weighted matching. The difference is that in our problem, we can view the whole vertex set as belonging to the initial solution, thus the solution of any algorithm is monotonously non-increasing with time.…”

Linear Programming in the Semi-streaming Model with Application to the Maximum Matching Problem

“…However, these results use random access significantly and do not translate to results in the semi-streaming model, and newer ideas were used in [10,23,35,9,8,7] to achieve results in the semi-streaming model. To improve upon the results in these papers, we need new and more powerful techniques.…”