7,517 research outputs found
Tight Approximation Algorithms For Geometric Bin Packing with Skewed Items
In the Two-dimensional Bin Packing (2BP) problem, we are given a set of rectangles of height and width at most one and our goal is to find an axis-aligned nonoverlapping packing of these rectangles into the minimum number of unit square bins. The problem admits no APTAS and the current best approximation ratio is 1.406 by Bansal and Khan [SODA\u2714]. A well-studied variant of the problem is Guillotine Two-dimensional Bin Packing (G2BP), where all rectangles must be packed in such a way that every rectangle in the packing can be obtained by recursively applying a sequence of end-to-end axis-parallel cuts, also called guillotine cuts. Bansal, Lodi, and Sviridenko [FOCS\u2705] obtained an APTAS for this problem. Let ? be the smallest constant such that for every set I of items, the number of bins in the optimal solution to G2BP for I is upper bounded by ? opt(I) + c, where opt(I) is the number of bins in the optimal solution to 2BP for I and c is a constant. It is known that 4/3 ? ? ? 1.692. Bansal and Khan [SODA\u2714] conjectured that ? = 4/3. The conjecture, if true, will imply a (4/3+?)-approximation algorithm for 2BP. According to convention, for a given constant ? > 0, a rectangle is large if both its height and width are at least ?, and otherwise it is called skewed. We make progress towards the conjecture by showing ? = 4/3 for skewed instance, i.e., when all input rectangles are skewed. Even for this case, the previous best upper bound on ? was roughly 1.692. We also give an APTAS for 2BP for skewed instance, though general 2BP does not admit an APTAS
On the Crepant Resolution Conjecture for Gromov-Witten Gravitational Ancestors in All Genera for Surface Singularities
We state a version of the crepant resolution conjecture for total ancestor
potentials for surface singularities, and reduce the conjecture to the quantum
McKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishing
conjecture for Hurwitz-Hodge integrals. In particular, for singularities of
type A, we prove the conjecture. We also suggest an approach towards a proof
for the general cases by Teleman's reconstruction theorem for semisimple
cohomological field theories.Comment: Typos and small mistakes correcte
Low-Temperature Structure of the Quarter-Filled Ladder Compound alpha'-NaV2O5
The low-temperature (LT) superstructure of -NaVO was
determined by synchrotron radiation x-ray diffraction. Below the phase
transition temperature associated with atomic displacement and charge ordering
at 34K, we observed the Bragg peak splittings, which evidence that the LT
structure is monoclinic. It was determined that the LT structure is
with the space group where and
represent the high temperature orthorhombic unit cell. The valence estimation
of V ions according to the bond valence sum method shows that the V sites are
clearly separated into two groups of V and V with a
charge ordering pattern. This LT structure is consistent with resonant x-ray
and NMR measurements, and strikingly contrasts to the LT structure previously
reported, which includes V sites.Comment: 4 pages, 3 figures, 1 tabl
Logic Programming with Default, Weak and Strict Negations
This paper treats logic programming with three kinds of negation: default,
weak and strict negations. A 3-valued logic model theory is discussed for logic
programs with three kinds of negation. The procedure is constructed for
negations so that a soundness of the procedure is guaranteed in terms of
3-valued logic model theory.Comment: 14 pages, to appear in Theory and Practice of Logic Programming
(TPLP
GMM Estimation of Affine Term Structure Models
This article investigates parameter estimation of affine term structure
models by means of the generalized method of moments. Exact moments of the
affine latent process as well as of the yields are obtained by using results
derived for p-polynomial processes. Then the generalized method of moments,
combined with Quasi-Bayesian methods, is used to get reliable parameter
estimates and to perform inference. After a simulation study, the estimation
procedure is applied to empirical interest rate data
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