Improved approximation bounds for Vector Bin Packing

In this paper we propose an improved approximation scheme for the Vector Bin Packing problem (VBP), based on the combination of (near-)optimal solution of the Linear Programming (LP) relaxation and a greedy (modified first-fit) heuristic. The Vector Bin Packing problem of higher dimension (d \geq 2) is not known to have asymptotic polynomial-time approximation schemes (unless P = NP). Our algorithm improves over the previously-known guarantee of (ln d + 1 + epsilon) by Bansal et al. [1] for higher dimensions (d > 2). We provide a {\theta}(1) approximation scheme for certain set of inputs for any dimension d. More precisely, we provide a 2-OPT algorithm, a result which is irrespective of the number of dimensions d.Comment: 15 pages, 3 algorithm

Inferring Concise Specifications of APIs

Modern software relies on libraries and uses them via application programming interfaces (APIs). Correct API usage as well as many software engineering tasks are enabled when APIs have formal specifications. In this work, we analyze the implementation of each method in an API to infer a formal postcondition. Conventional wisdom is that, if one has preconditions, then one can use the strongest postcondition predicate transformer (SP) to infer postconditions. However, SP yields postconditions that are exponentially large, which makes them difficult to use, either by humans or by tools. Our key idea is an algorithm that converts such exponentially large specifications into a form that is more concise and thus more usable. This is done by leveraging the structure of the specifications that result from the use of SP. We applied our technique to infer postconditions for over 2,300 methods in seven popular Java libraries. Our technique was able to infer specifications for 75.7% of these methods, each of which was verified using an Extended Static Checker. We also found that 84.6% of resulting specifications were less than 1/4 page (20 lines) in length. Our technique was able to reduce the length of SMT proofs needed for verifying implementations by 76.7% and reduced prover execution time by 26.7%

Towards a chiral gauge theory by deconstruction in AdS5

We describe an implementation of a deconstructed gauge theory with charged fermions defined on an interval in five dimensional AdS space. The four dimensional slices are Minkowski, and the end slices support four dimensional chiral zero modes. In such a theory, the energy scales warp down as we move along the fifth dimension. If we augment this theory with localized neutral 4-dimensional Majorana fermions on the low energy end, and implement a Higgs mechanism there, we can arrange the theory such that the lightest gauge boson mode and the chiral mode on the wall at the high energy end are parametrically lighter than all the other states in the theory. If this semiclassical construction does not run into problems at the quantum level, this may provide an explicit construction of a chiral gauge theory. Instanton effects are expected to make the gauge boson heavy only if the resulting effective theory is anomalous.Comment: 6 pages, 3 figures, presented at Lattice2005(Chiral fermions), Dublin, July 25-30, 2005, to appear in Proceedings of Scienc

Anharmonic oscillators and the null bootstrap

We employ the technique of perturbative analytic null bootstrap to obtain the energy eigenvalues and ladder operators of the sextic anharmonic oscillator up to second order in the coupling. We confirm our results by deriving the same from traditional perturbation theory. We further perform the bootstrap approach on non-Hermitian PT symmetric Hamiltonians, focusing on the shifted harmonic oscillator and the celebrated cubic anharmonic oscillator.Comment: v2:references added, minor changes in the presentation at a few place

Anyonic correlation functions in Chern-Simons matter theories

We show that in spinor-helicity variables, two-point and three-point functions in Chern-Simons matter theories can be obtained from either the free boson theory or the free fermion theory with an appropriate coupling constant dependent anyonic phase factor which interpolates nicely between the free fermion theory and the free boson theory. For specific examples of four-point functions involving spinning operators we argue that the correlators can again be reproduced from the free theory with an appropriate phase factor.Comment: 23 pages, v2 : Subsection 5.4 on $\langle TTTT\rangle$ added. Added details of the strategy employed in Section