827 research outputs found
Parallel String Sample Sort
We discuss how string sorting algorithms can be parallelized on modern
multi-core shared memory machines. As a synthesis of the best sequential string
sorting algorithms and successful parallel sorting algorithms for atomic
objects, we propose string sample sort. The algorithm makes effective use of
the memory hierarchy, uses additional word level parallelism, and largely
avoids branch mispredictions. Additionally, we parallelize variants of multikey
quicksort and radix sort that are also useful in certain situations.Comment: 34 pages, 7 figures and 12 table
Active auxin uptake by zucchini membrane vesicles: quantitation using ESR volume and delta pH determinations.
Maximum weight cycle packing in directed graphs, with application to kidney exchange programs
Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration
EFX Allocations: Simplifications and Improvements
The existence of EFX allocations is a fundamental open problem in discretefair division. Given a set of agents and indivisible goods, the goal is todetermine the existence of an allocation where no agent envies anotherfollowing the removal of any single good from the other agent's bundle. Sincethe general problem has been illusive, progress is made on two fronts: proving existence when the number of agents is small, proving existenceof relaxations of EFX. In this paper, we improve results on both fronts (andsimplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting onlyone agent to have an MMS-feasible valuation function (a strict generalizationof nice-cancelable valuation functions introduced by Berger et al. whichsubsumes additive, budget-additive and unit demand valuation functions). Theother agents may have any monotone valuation functions. Our proof technique issignificantly simpler and shorter than the proof by Chaudhury et al. onexistence of EFX allocations when there are three agents with additivevaluation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFXallocations and EFX allocations with few unallocated goods (charity). Chaudhuryet al. showed the existence of -EFX allocation with charity by establishing a connection to aproblem in extremal combinatorics. We improve their result and prove theexistence of -EFX allocations with charity. In fact, some of our techniques can be usedto prove improved upper-bounds on a problem in zero-sum combinatoricsintroduced by Alon and Krivelevich.<br
Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D Random-Bond Ising Model
The statistics of the ground-state and domain-wall energies for the
two-dimensional random-bond Ising model on square lattices with independent,
identically distributed bonds of probability of and of
are studied. We are able to consider large samples of up to
spins by using sophisticated matching algorithms. We study
systems, but we also consider samples, for different aspect ratios
. We find that the scaling behavior of the ground-state energy and
its sample-to-sample fluctuations inside the spin-glass region () are characterized by simple scaling functions. In particular, the
fluctuations exhibit a cusp-like singularity at . Inside the spin-glass
region the average domain-wall energy converges to a finite nonzero value as
the sample size becomes infinite, holding fixed. Here, large finite-size
effects are visible, which can be explained for all by a single exponent
, provided higher-order corrections to scaling are included.
Finally, we confirm the validity of aspect-ratio scaling for : the
distribution of the domain-wall energies converges to a Gaussian for ,
although the domain walls of neighboring subsystems of size are
not independent.Comment: 11 pages with 15 figures, extensively revise
Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
We study ground-state properties of the two-dimensional random-bond Ising
model with couplings having a concentration of antiferromagnetic
and of ferromagnetic bonds. We apply an exact matching algorithm which
enables us the study of systems with linear dimension up to 700. We study
the behavior of the domain-wall energies and of the magnetization. We find that
the paramagnet-ferromagnet transition occurs at compared to
the concentration at the Nishimory point, which means that the
phase diagram of the model exhibits a reentrance. Furthermore, we find no
indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe
One-variable word equations in linear time
In this paper we consider word equations with one variable (and arbitrary
many appearances of it). A recent technique of recompression, which is
applicable to general word equations, is shown to be suitable also in this
case. While in general case it is non-deterministic, it determinises in case of
one variable and the obtained running time is O(n + #_X log n), where #_X is
the number of appearances of the variable in the equation. This matches the
previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a
couple of heuristics as well as more detailed time analysis the running time is
lowered to O(n) in RAM model. Unfortunately no new properties of solutions are
shown.Comment: submitted to a journal, general overhaul over the previous versio
Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation
Hot dense capsule implosions driven by z-pinch x-rays have been measured for
the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter
gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom
spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4
x10^23 cm-3 electron density. Spectra from multiple directions provide core
symmetry estimates. Computer simulations agree well with the peak compression
values of Te, ne, and symmetry, indicating reasonable understanding of the
hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
We consider geometric instances of the Maximum Weighted Matching Problem
(MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000
vertices. Making use of a geometric duality relationship between MWMP, MTSP,
and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields
in near-linear time solutions as well as upper bounds. Using various
computational tools, we get solutions within considerably less than 1% of the
optimum.
An interesting feature of our approach is that, even though an FWP is hard to
compute in theory and Edmonds' algorithm for maximum weighted matching yields a
polynomial solution for the MWMP, the practical behavior is just the opposite,
and we can solve the FWP with high accuracy in order to find a good heuristic
solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental
Algorithms, 200
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