Algorithmics of Matching Under Preferences - download pdf or read online

By David F Manlove

ISBN-10: 9814425249

ISBN-13: 9789814425247

Matching issues of personal tastes are throughout us: they come up whilst brokers search to be allotted to each other at the foundation of ranked personal tastes over power results. effective algorithms are wanted for generating matchings that optimise the pride of the brokers in response to their choice lists.

in recent times there was a pointy raise within the examine of algorithmic features of matching issues of personal tastes, partially reflecting the growing to be variety of functions of those difficulties world wide. the significance of the learn region was once recognized in 2012 in the course of the award of the Nobel Prize in monetary Sciences to Alvin Roth and Lloyd Shapley.

This publication describes an important ends up in this sector, offering a well timed replace to The solid Marriage challenge: constitution and Algorithms (D Gusfield and R W Irving, MIT Press, 1989) in reference to reliable matching difficulties, while additionally broadening the scope to incorporate matching issues of personal tastes below more than a few substitute optimality standards.

Readership: scholars and execs attracted to algorithms, specifically within the examine of algorithmic facets of matching issues of personal tastes.

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Extra info for Algorithmics of Matching Under Preferences

Example text

We summarise these observations as follows. 9 ([235, 261]). Given an instance of hr, the RGS algorithm constructs, in O(m) time, the unique resident-optimal stable matching, where m is the number of acceptable resident–hospital pairs. The resident-optimal stable matching Ma is worst-possible for the hospitals in a precise sense: if M is any other stable matching then every hospital hj ∈ H prefers each resident in M (hj ) to each resident in Ma (hj )\M (hj ) [261, Sec. 5]. A counterpart of the RGS algorithm, known as the hospital-oriented Gale–Shapley algorithm, or HGS algorithm for short, involves hospitals offering posts to residents.

3 Bipartite matching problems with one-sided preferences The House Allocation problem (ha) (defined in Sec. 2) [301,595,5] is the variant of sm in which the women do not have preference lists over the men. The men are now referred to as applicants and the women are referred to as houses. The problem name stems from the application where students are assigned to campus housing, based on their preferences over the available accommodation. This is accomplished using a centralised matching scheme in a number of universities including Carnegie-Mellon University, Duke University, the University of Michigan, Northwestern University and the University of Pennsylvania in the US [142], and the Technion in Israel [474].

A many–one extension of ha, called the Capacitated House Allocation problem (cha) arises when each house can accommodate multiple applicants up to some fixed capacity. cha can also be regarded as the variant of hr in which hospitals do not have preference lists over residents. In the context of ha and cha, only applicants have preferences over houses, so the notion of stability is not relevant. Other optimality criteria have been formulated in the literature, including Pareto optimality, popularity and profile-based optimality.

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Algorithmics of Matching Under Preferences by David F Manlove

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