455 research outputs found
Efficient algorithms for three-dimensional axial and planar random assignment problems
Beautiful formulas are known for the expected cost of random two-dimensional
assignment problems, but in higher dimensions even the scaling is not known. In
three dimensions and above, the problem has natural "Axial" and "Planar"
versions, both of which are NP-hard. For 3-dimensional Axial random assignment
instances of size , the cost scales as , and a main result of
the present paper is a linear-time algorithm that, with high probability, finds
a solution of cost . For 3-dimensional Planar assignment, the
lower bound is , and we give a new efficient matching-based
algorithm that with high probability returns a solution with cost
Diszkrét matematika = Discrete mathematics
A pĂĄlyĂĄzat rĂ©sztvevĆi igen aktĂvak voltak a 2006-2008 Ă©vekben. Nemcsak sok eredmĂ©nyt Ă©rtek el, miket több mint 150 cikkben publikĂĄltak, eredmĂ©nyesen nĂ©pszerƱsĂtettĂ©k azokat. Több mint 100 konferenciĂĄn vettek rĂ©szt Ă©s adtak elĆ, felerĂ©szben meghĂvott, vagy plenĂĄris elĆadĂłkĂ©nt. HagyomĂĄnyos grĂĄfelmĂ©let Több extremĂĄlis grĂĄfproblĂ©mĂĄt oldottunk meg. Ăj eredmĂ©nyeket kaptunk Ramsey szĂĄmokrĂłl, globĂĄlis Ă©s lokĂĄlis kromatikus szĂĄmokrĂłl, Hamiltonkörök lĂ©tezĂ©sĂ©sĂ©rĆl. a crossig numberrĆl, grĂĄf kapacitĂĄsokrĂłl Ă©s kizĂĄrt rĂ©szgrĂĄfokrĂłl. VĂ©letlen grĂĄfok, nagy grĂĄfok, regularitĂĄsi lemma Nagy grĂĄfok "hasonlĂłsĂĄgait" vizsgĂĄltuk. KĂŒlönfĂ©le metrikĂĄk ekvivalensek. Ć°j eredemĂ©nyeink: Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit. HipergrĂĄfok, egyĂ©b kombinatorika Ăj Sperner tipusĂș tĂ©telekte kaptunk, aszimptotikusan meghatĂĄrozva a halmazok max szĂĄmĂĄt bizonyos kizĂĄrt struktĆrĂĄk esetĂ©n. Több esetre megoldottuk a kizĂĄrt hipergrĂĄf problĂ©mĂĄt is. ElmĂ©leti szĂĄmĂtĂĄstudomĂĄny Ăj ujjlenyomat kĂłdokat Ă©s bioinformatikai eredmĂ©nyeket kaptunk. | The participants of the project were scientifically very active during the years 2006-2008. They did not only obtain many results, which are contained in their more than 150 papers appeared in strong journals, but effectively disseminated them in the scientific community. They participated and gave lectures in more than 100 conferences (with multiplicity), half of them were plenary or invited talks. Traditional graph theory Several extremal problems for graphs were solved. We obtained new results for certain Ramsey numbers, (local and global) chromatic numbers, existence of Hamiltonian cycles crossing numbers, graph capacities, and excluded subgraphs. Random graphs, large graphs, regularity lemma The "similarities" of large graphs were studied. We show that several different definitions of the metrics (and convergence) are equivalent. Several new results like the Hereditary Property Testing, Inverse Counting Lemma and the Uniqueness of Hypergraph Limit were proved Hypergraphs, other combinatorics New Sperner type theorems were obtained, asymptotically determining the maximum number of sets in a family of subsets with certain excluded configurations. Several cases of the excluded hypergraph problem were solved. Theoretical computer science New fingerprint codes and results in bioinformatics were found
The FermiâPastaâUlam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents
open3noFPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include
the usual -model, perturbations of Toda include the usual model. In this paper we explore and compare two
families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each
model, the maximal Lyapunov exponent . More precisely, we consider statistically typical trajectories and study the asymptotics
of for large (the number of particles) and small (the specific energy ), and find, for all models, asymptotic
power laws , and depending on the model. The asymptotics turns out to be, in general, rather slow, and
producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of introduced
by Casetti, Livi and Pettini, originally formulated for the -model. With great evidence the theory extends successfully to
all models of the linear hierarchy, but not to models close to Toda.openBenettin, G.*; Pasquali, S.; Ponno, A.Benettin, G.; Pasquali, S.; Ponno, A
More Natural Models of Electoral Control by Partition
"Control" studies attempts to set the outcome of elections through the
addition, deletion, or partition of voters or candidates. The set of benchmark
control types was largely set in the seminal 1992 paper by Bartholdi, Tovey,
and Trick that introduced control, and there now is a large literature studying
how many of the benchmark types various election systems are vulnerable to,
i.e., have polynomial-time attack algorithms for.
However, although the longstanding benchmark models of addition and deletion
model relatively well the real-world settings that inspire them, the
longstanding benchmark models of partition model settings that are arguably
quite distant from those they seek to capture.
In this paper, we introduce--and for some important cases analyze the
complexity of--new partition models that seek to better capture many real-world
partition settings. In particular, in many partition settings one wants the two
parts of the partition to be of (almost) equal size, or is partitioning into
more than two parts, or has groups of actors who must be placed in the same
part of the partition. Our hope is that having these new partition types will
allow studies of control attacks to include such models that more realistically
capture many settings
Efficient algorithms for three-dimensional axial and planar random assignment problems
Beautiful formulas are known for the expected cost of random two-dimensional assignment problems, but in higher dimensions even the scaling is not known. In three dimensions and above, the problem has natural âAxialâ and âPlanarâ versions, both of which are NP-hard. For 3-dimensional Axial random assignment instances of size n, the cost scales as Ω(1/ n), and a main result of the present paper is a linear-time algorithm that, with high probability, finds a solution of cost O(nâ1+o(1)). For 3-dimensional Planar assignment, the lower bound is Ω(n), and we give a new efficient matching-based algorithm that with high probability returns a solution with cost O(n log n)
More on quasi-random graphs, subgraph counts and graph limits
We study some properties of graphs (or, rather, graph sequences) defined by
demanding that the number of subgraphs of a given type, with vertices in
subsets of given sizes, approximatively equals the number expected in a random
graph. It has been shown by several authors that several such conditions are
quasi-random, but that there are exceptions. In order to understand this
better, we investigate some new properties of this type. We show that these
properties too are quasi-random, at least in some cases; however, there are
also cases that are left as open problems, and we discuss why the proofs fail
in these cases.
The proofs are based on the theory of graph limits; and on the method and
results developed by Janson (2011), this translates the combinatorial problem
to an analytic problem, which then is translated to an algebraic problem.Comment: 35 page
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