Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Observations on the ossification centres of Trichopodus trichopterus (Pall.)

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The development of the chondrocranium in Trichopodus trichopterus (Pall.)

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Electronic structure of spin-mixed iron(III) porphyrins: a proton magnetic resonance study

The proton magnetic resonance studies on the perchlorato iron(III) porphyrins in solution have been described. The isotropic proton shifts in these complexes show anomalous temperature dependence, consistent with its unusual properties in solid state. The NMR data have been analysed on the basis of a crystal field theory which includes lower asymmetric field and spin-orbit interaction. The analysis brings out that the ground state of the ferric ion in these porphyrin complexes exhibits the novel spin-mixed behaviour with spin-mixing between S = 3/2 and S = 5/2. The ground state is predominantly a spin quartet with the spin sextet being a very close lying excited state. Such a spin situation and spin-mixing have been speculated for the ferric ion in some ferricytochromec'. The present paper also highlights that the isotropic proton shift is very sensitive to the electronic structure of the metal ion and hence can be used to determine the electronic structure of the metal ion in heme systems in solution

Robustness against parametric noise of non ideal holonomic gates

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev.

Particle current in symmetric exclusion process with time-dependent hopping rates

In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two neighboring sites of a closed ring vary periodically in time and have a relative phase difference, there is a net DC current which decreases inversely with the system size. In this work, we simplify and generalize our earlier treatment. We study a model where hopping rates at all sites vary periodically in time, and show that for certain choices of relative phases, a DC current of order unity can be obtained. Our results are obtained using a perturbation theory in the amplitude of the time-dependent part of the hopping rate. We also present results obtained in a sudden approximation that assumes large modulation frequency.Comment: 17 pages, 2 figure