Book ChapterDOI
Competitive Weighted Matching in Transversal Matroids
Nedialko B. Dimitrov,C. Greg Plaxton +1 more
- pp 397-408
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An algorithm is presented that processes a uniformly random permutation of the left-vertices, one left-vertex at a time, and the weight of the matching returned is within a constant factor of that of a maximum weight matching.Abstract:
Consider a bipartite graph with a set of left-vertices and a set of right-vertices. All the edges adjacent to the same left-vertex have the same weight. We present an algorithm that, given the set of right-vertices and the number of left-vertices, processes a uniformly random permutation of the left-vertices, one left-vertex at a time. In processing a particular left-vertex, the algorithm either permanently matches the left-vertex to a thus-far unmatched right-vertex, or decides never to match the left-vertex. The weight of the matching returned by our algorithm is within a constant factor of that of a maximum weight matching.read more
Citations
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Book
Online Matching and Ad Allocation
TL;DR: This monograph surveys the key problems, models and algorithms from online matchings, as well as their implication in the practice of ad allocation, to provide a classification of the problems, techniques and algorithms in this area.
Proceedings ArticleDOI
Matroid prophet inequalities
TL;DR: In this paper, the prophet inequality of Krengel, Sucheston, and Garling has been generalized to the matroid setting, where the prophet and the gambler are allowed to make more than one selection subject to a matroid constraint.
Journal ArticleDOI
Online auctions and generalized secretary problems
TL;DR: This work presents generalized secretary problems as a framework for online auctions, and presents surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms.
Book ChapterDOI
Constrained non-monotone submodular maximization: offline and secretary algorithms
TL;DR: In this article, a greedy-based constant factor algorithm for non-monotone submodular maximization subject to a knapsack constraint and a secretary constraint was proposed.
Proceedings ArticleDOI
Online vertex-weighted bipartite matching and single-bid budgeted allocations
TL;DR: In this paper, an optimal (1−1/e)-competitive randomized algorithm for general vertex weights was proposed, which is the first known generalization of the algorithm in this model and provides new insights into the role of randomization in online allocation problems.
References
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Book
Online Computation and Competitive Analysis
Allan Borodin,Ran El-Yaniv +1 more
TL;DR: This book discusses competitive analysis and decision making under uncertainty in the context of the k-server problem, which involves randomized algorithms in order to solve the problem of paging.
Proceedings ArticleDOI
An optimal algorithm for on-line bipartite matching
TL;DR: This work applies the general approach to data structures, bin packing, graph coloring, and graph coloring to bipartite matching and shows that a simple randomized on-line algorithm achieves the best possible performance.
Journal ArticleDOI
Who Solved the Secretary Problem
TL;DR: The object of this article is to give a fresh view of the origins of the problem, touching upon Cayley and Kepler, and review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment.
Journal ArticleDOI
The Secretary Problem and its Extensions: A Review
TL;DR: In this article, the development of what has come to be known as the secretary problem is traced from its origins in the early 1960's and all published work to date on the problem and its extensions is reviewed.