248 research outputs found
Berge Sorting
In 1966, Claude Berge proposed the following sorting problem. Given a string
of alternating white and black pegs on a one-dimensional board consisting
of an unlimited number of empty holes, rearrange the pegs into a string
consisting of white pegs followed immediately by
black pegs (or vice versa) using only moves which
take 2 adjacent pegs to 2 vacant adjacent holes. Avis and Deza proved that the
alternating string can be sorted in such {\em Berge
2-moves} for . Extending Berge's original problem, we consider the
same sorting problem using {\em Berge -moves}, i.e., moves which take
adjacent pegs to vacant adjacent holes. We prove that the alternating
string can be sorted in Berge 3-moves for
and in Berge 3-moves for
, for . In general, we conjecture that, for any
and large enough , the alternating string can be sorted in
Berge -moves. This estimate is tight as
is a lower bound for the minimum number of required
Berge -moves for and .Comment: 10 pages, 2 figure
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Heterogeneous Tiebout communities with private production and anonymous crowding
his paper examines, in the context of a multiple types of consumers, a set of necessary and sufficient conditions under which equilibrium and optimum exist, and involve mixing types of consumers in jurisdictions. Pricing includes visa permits for entry. Following Berglas (1976), we assume anonymous crowding and complementarities in production. For a large economy, we prove existence of equilibrium and the first and second welfare theorems. Our simultaneous optimization approach provides a new technique for showing existence of equilibrium in local public good economies with local production and a continuum of agents.Local public goods, Collaborative production, Wages, Anonymous crowding, Visa permits, Societal stratification, Heterogeneous Tiebout communities, Generalized game
Weighted Fractional and Integral k-Matching in Hypergraphs
We consider the problem of finding polynomial-time approximations of maximal weighted k-matchings in a hypergraph and investigate the relationship between the integral and fractional maxima of the corresponding 0-1 integer linear program and its LP-relaxation. We extend results of Raghavan, who gave a deterministic approximation algorithm for unweighted k-matching, to the weighted case and compare the so obtained lower bound for the ratio of the integer and fractional maximum with a lower bound of Aharoni, Erdös and Linial
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