An adjustable linear time parallel algorithm for maximum weight bipartite matching

Toward Expressive and Scalable Sponsored Search Auctions

“…To make the problem scalable, we need it to be linear in n, the number of advertisers. There are parallel algorithms for maximum-weight matching [15], but these require prohibitively large numbers (typically Ω(n 2 )) of processing units in order to achieve linear running time.…”

“…If we have a binary tree network with p nodes, then the total running time becomes O( n p k log k + k log p + k 5 ). Finally the O(k 5 ) part of the algorithm (i.e., the part resulting from running the Hungarian algorithm on the reduced bipartite graph) can be reduced to O(k 2 ) using a parallel algorithm, such as in [15]. The number of parallel processing units required is O(k 5 ), which is independent of n.…”

Conflict Resolution for User-Selected Names in Collaborative Systems

“…Not all possible graphs NS have a perfect matching, although all graphs have a matching that connects the largest number of names and objects. To find the best matching in terms of the number of reused names (or bindings) we need to find this latter, solving the so-called maximum weight bipartite matching (MWBM) problem [10].…”

“…Several efficient algorithms for the MWBM problem exist both in the sequential [14] and parallel [10] flavor. Once a MWBM has been found, for every unnamed object in NSMWBM, if any, the system chooses a unique name, obtaining a prefect matching NS*.…”