9,751 research outputs found
Tilings in randomly perturbed dense graphs
A perfect -tiling in a graph is a collection of vertex-disjoint copies
of a graph in that together cover all the vertices in . In this
paper we investigate perfect -tilings in a random graph model introduced by
Bohman, Frieze and Martin in which one starts with a dense graph and then adds
random edges to it. Specifically, for any fixed graph , we determine the
number of random edges required to add to an arbitrary graph of linear minimum
degree in order to ensure the resulting graph contains a perfect -tiling
with high probability. Our proof utilises Szemer\'edi's Regularity lemma as
well as a special case of a result of Koml\'os concerning almost perfect
-tilings in dense graphs.Comment: 19 pages, to appear in CP
Hyperbolic intersection graphs and (quasi)-polynomial time
We study unit ball graphs (and, more generally, so-called noisy uniform ball
graphs) in -dimensional hyperbolic space, which we denote by .
Using a new separator theorem, we show that unit ball graphs in
enjoy similar properties as their Euclidean counterparts, but in one dimension
lower: many standard graph problems, such as Independent Set, Dominating Set,
Steiner Tree, and Hamiltonian Cycle can be solved in
time for any fixed , while the same problems need
time in . We also show that these algorithms in
are optimal up to constant factors in the exponent under ETH.
This drop in dimension has the largest impact in , where we
introduce a new technique to bound the treewidth of noisy uniform disk graphs.
The bounds yield quasi-polynomial () algorithms for all of the
studied problems, while in the case of Hamiltonian Cycle and -Coloring we
even get polynomial time algorithms. Furthermore, if the underlying noisy disks
in have constant maximum degree, then all studied problems can
be solved in polynomial time. This contrasts with the fact that these problems
require time under ETH in constant maximum degree
Euclidean unit disk graphs.
Finally, we complement our quasi-polynomial algorithm for Independent Set in
noisy uniform disk graphs with a matching lower bound
under ETH. This shows that the hyperbolic plane is a potential source of
NP-intermediate problems.Comment: Short version appears in SODA 202
Embedding graphs having Ore-degree at most five
Let and be graphs on vertices, where is sufficiently large.
We prove that if has Ore-degree at most 5 and has minimum degree at
least then Comment: accepted for publication at SIAM J. Disc. Mat
The Public Value Scorecard: A Rejoinder and an Alternative to "Strategic Performance Measurement and Management in Non-Profit Organizations"
Robert Kaplan's Balanced Scorecard has played an important and welcome role in the nonprofit world as nonprofit organizations have struggled to measure their performance. Many nonprofit organizations have taken both general inspiration and specific operational guidance from the ideas advanced in this important work. Their pioneering efforts to apply these concepts to their own particular settings have added a layer of richness to the important concepts. Given the great contribution of this work to helping nonprofits meet the challenge of measuring their performance, it seems both ungracious and unhelpful to criticize it. Yet, as I review the concepts of the Balanced Scorecard, and look closely at the cases of organizations that have tried to use these concepts to measure their performance, I believe that some systematic confusions arise. Further, I think the source of these confusions lies in the fact the basic concepts of the Balanced Scorecard have not been sufficiently adapted from the private, for-profit world where they were born to the world of the nonprofit manager where they are now being applied. Finally, I think a different way of thinking about nonprofit strategy and linking that to performance measurement exists that is simpler that and more reliable for nonprofit organizations to rely upon. The purpose of this paper is to set out these contrarian ideas. This publication is Hauser Center Working Paper No. 18. The Hauser Center Working Paper Series was launched during the summer of 2000. The Series enables the Hauser Center to share with a broad audience important works-in-progress written by Hauser Center scholars and researchers
Summary of the recent short-haul systems studies
The results of several NASA sponsored high density short haul air transportation systems studies are reported as well as analyzed. Included are the total STOL systems analysis approach, a companion STOL composites study conducted in conjunction with STOL systems studies, a STOL economic assessment study, an evaluation of STOL aircraft with and without externally blown flaps, an alternative STOL systems for the San Francisco Bay Area, and the quiet, clean experimental engine studies. Assumptions and results of these studies are summarized, their differences, analyzed, and the results compared with those in-house analyses performed by the Systems Studies Division of the NASA-Ames Research Center. Pertinent conclusions are developed and the more significant technology needs for the evaluation of a viable short haul transportation system are identified
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