Pareto optimality in many-to-many matching problems

Consider a many-to-many matching market that involves two finite disjoint sets, a set A of applicants and a set C of courses. Each applicant has preferences on the different sets of courses she can attend, while each course has a quota of applicants that it can admit. In this paper, we examine Pareto optimal matchings (briefly POM) in the context of such markets, that can also incorporate additional constraints, e.g., each course bearing some cost and each applicant having a limited budget available. We provide necessary and sufficient conditions for a many-to-many matching to be Pareto optimal and show that checking whether a given matching is Pareto optimal can be accomplished in 0(1 A 12 I C 12) time. Moreover, we provide a generalized version of serial dictatorship, which can be used to obtain any many-to-many POM. We also study some structural questions related to POM. We show that, unlike in the one-to-one case, finding a maximum cardinality POM is NP-hard for many-to-many markets. (C) 2014 Elsevier B.V. All rights reserved

Parameterized Directed kk-Chinese Postman Problem and kk Arc-Disjoint Cycles Problem on Euler Digraphs

In the Directed $k$-Chinese Postman Problem ($k$-DCPP), we are given a connected weighted digraph $G$ and asked to find $k$ non-empty closed directed walks covering all arcs of $G$ such that the total weight of the walks is minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128) asked for the parameterized complexity of $k$-DCPP when $k$ is the parameter. We prove that the $k$-DCPP is fixed-parameter tractable. We also consider a related problem of finding $k$ arc-disjoint directed cycles in an Euler digraph, parameterized by $k$. Slivkins (ESA 2003) showed that this problem is W[1]-hard for general digraphs. Generalizing another result by Slivkins, we prove that the problem is fixed-parameter tractable for Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler digraphs remains W[1]-hard even for Euler digraphs

Inequities and inadequacies of local taxation: principles and practice of unitary and federal countries with special reference to great Britain and the United States

The present study is an attempt both to analyse and illustrate the financial and economic implications of the intergovernmental relations in unitary and federal polities. The investigation is confined to the baneful or conflicting impact of the various interrelationships.The Prologue clarifies certain basic notions and trends and summarizes the writer's views. Part One on Inequities, deals, in the first chapter, with fiscal inequities and inequalities and in the second chapter, with overlapping and multiple taxation.Part Two on Inadequacies, is composed of two chapters. The first tackles the tax revenue deficiencies of the junior authorities. The second chapter expounds the conflicts which are prone to arise between local and national financial policies.Part Three on Intergovernmental Fiscal Co-ordination, is also an epilogue. It sets out diverse means of inter-local and notably central-local financial co-ordination. Various proposals are made

Spatial analysis of housing markets using the hedonic approach with geographic information systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 1994.Includes bibliographical references (leaves 181-188).by Lijian Chen.Ph.D