Online Maximum k-Coverage

We study an online model for the maximum k-vertex-coverage problem, where given a graph G = (V,E) and an integer k, we ask for a subset A ⊆ V, such that |A | = k and the number of edges covered by A is maximized. In our model, at each step i, a new vertex vi is revealed, and we have to decide whether we will keep it or discard it. At any time of the process, only k vertices can be kept in memory; if at some point the current solution already contains k vertices, any inclusion of any new vertex in the solution must entail the irremediable deletion of one vertex of the current solution (a vertex not kept when revealed is irremediably deleted). We propose algorithms for several natural classes of graphs (mainly regular and bipartite), improving on an easy 1/2-competitive ratio. We next settle a set-version of the problem, called maximum k-(set)-coverage problem. For this problem we present an algorithm that improves upon former results for the same model for small and moderate values of k

Fixed-Parameter Algorithms in Analysis of Heuristics for Extracting Networks in Linear Programs

We consider the problem of extracting a maximum-size reflected network in a linear program. This problem has been studied before and a state-of-the-art SGA heuristic with two variations have been proposed. In this paper we apply a new approach to evaluate the quality of SGA\@. In particular, we solve majority of the instances in the testbed to optimality using a new fixed-parameter algorithm, i.e., an algorithm whose runtime is polynomial in the input size but exponential in terms of an additional parameter associated with the given problem. This analysis allows us to conclude that the the existing SGA heuristic, in fact, produces solutions of a very high quality and often reaches the optimal objective values. However, SGA contain two components which leave some space for improvement: building of a spanning tree and searching for an independent set in a graph. In the hope of obtaining even better heuristic, we tried to replace both of these components with some equivalent algorithms. We tried to use a fixed-parameter algorithm instead of a greedy one for searching of an independent set. But even the exact solution of this subproblem improved the whole heuristic insignificantly. Hence, the crucial part of SGA is building of a spanning tree. We tried three different algorithms, and it appears that the Depth-First search is clearly superior to the other ones in building of the spanning tree for SGA. Thereby, by application of fixed-parameter algorithms, we managed to check that the existing SGA heuristic is of a high quality and selected the component which required an improvement. This allowed us to intensify the research in a proper direction which yielded a superior variation of SGA

First Observation of Coherent π0\pi^0 Production in Neutrino Nucleus Interactions with Eν<E_{\nu}< 2 GeV

The MiniBooNE experiment at Fermilab has amassed the largest sample to date of $\pi^0$s produced in neutral current (NC) neutrino-nucleus interactions at low energy. This paper reports a measurement of the momentum distribution of $\pi^0$s produced in mineral oil (CH$_2$) and the first observation of coherent $\pi^0$ production below 2 GeV. In the forward direction, the yield of events observed above the expectation for resonant production is attributed primarily to coherent production off carbon, but may also include a small contribution from diffractive production on hydrogen. Integrated over the MiniBooNE neutrino flux, the sum of the NC coherent and diffractive modes is found to be (19.5 $\pm$1.1 (stat) $\pm$2.5 (sys))% of all exclusive NC $\pi^0$ production at MiniBooNE. These measurements are of immediate utility because they quantify an important background to MiniBooNE's search for $\nu_{\mu} \to \nu_e$ oscillations.Comment: Submitted to Phys. Lett.

Maximum-Weight Independent Set is as "Well-Approximated" as the Unweighted One.

We devise an approximation-preserving reduction of expansion O between weighted and unweighted versions of a class of problems called weighted hereditary induced-subgraph maximisation problems. This allows us to perform a first improvement of the best approximation ratio for the weighted independent set problem.MATHEMATICAL ANALYSIS ; PROBABILITY ; WEIGHT

Towards a General Formal Framework for Polynomial Approximation (some Constitutive Elements of a New Problematics).

We draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results can be expressed within it.MATHEMATICAL ANALYSIS ; PROBABILITY

Towards a General Formal Framework for Polynomial Approximation (Concepts and Examples).

In a first time we draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results can be expressed within it. Next, we use the framework introduced to obatin approximation results for a number of NP-hard problems.APPROXIMATION ; HEREDITY ; MAXIMISATION

Maximizing the Number of Unused Bins.

We analyze the approximation behaviour of some of the best-known polynomial time approximation algorithms for bin-packing under an approximation criterion, called differential ratio. This measure has originally been introduced by Ausiello, D'Atri and Protasi and more recently revisited, in a more systematic way, by the first and the third authors of the present paper.BEHAVIOUR ; MATHEMATICAL ANALYSIS ; PROBABILITY

On-line Maximum-order Induced Hereditary Subgraph Problems.

We first study the competitivity ratio for the on-line version of the problem of finding a maximum-order induced subgraph satisfying some hereditary property, under the hypothesis that the input graph is revealed by clusters. Next, we focus ourselves on two of the most known instantiations of this problem, the maximum independent set and the maximum clique. Finally, we study a variant of the on-line maximum-weight induced hereditary subgraph problem.COMPETITION ; HEREDITY ; HEREDITARY PROPERTY

Circular Cutting Problem: A Simulated Annealing Approach.

OPTIMIZATION

Lower bounds on the approximation ratios of leading heuristics for the single machine total tardiness problem

The weakly NP-hard single-machine total tardiness scheduling problem has been extensively studied in the last decades. Various heuristics have been proposed to efficiently solve in practice a problem for which a fully polynomial time approximation scheme exists (though with complexity O(n 7/E)). In this note, we show that all known constructive heuristics for the problem, namely AU, MDD, PSK, WI, COVERT, NBR, present arbitrarily bad approximation ratios. The same behavior is shown by the decomposition heuristics DEC/EDD, DEC/MDD, DEC/PSK, and DEC/WI.ou