souci d'allier la proposition d'idées originales, qui ressortent du cadre de l'application simple, et de la concrétisation fiable de cesdernì eres. Y arriver est une chose d'extrêmement gratifiante. Leséchanges que nous avons eu m'ont toujours beaucoup apportés.

Sticker model is imitated by using set, variable length vector and biochemistry operator instead of tube, memory strand and biochemistry experiment for the first time. Batch separation operator and electrophoresis operator are first put forward based on DNA algorithm of Set Covering Problem (SCP) based on sticker model. Expression way, calculation method and basic properties of variable length ...

1. R2-phenomena . Our set theoretic notation will be standard with one exception . Since this paper is largely concerned with powers of ordinals, the symbol ~" will always denote ordinal exponentiation for ordinals ~, 11 . Thus, in particular, if fl--a, then cos is an ordinal <coy+1 . When we use cardinal exponentiation we shall either say so or, if there is no danger of confusion, we write 2 1...

The present study introduced a novel hierarchical hub set covering problem with capacity constraints. This study showed the significance of fixed charge costs for locating facilities, assigning hub links and designing a productivity network. The proposed model employs mixed integer programming to locate facilities and establish links between nodes according to the travel time between an origin-...

Several familiar problems in extremal set theory can be cast as questions about the maximum possible size of an independent set defined on a suitable graph, about the total number of independent sets in such graphs, or about enumeration of the maximal independent sets. Here we find bounds on the number of maximal independent sets in the covering graph of a hypercube. © 2010 Elsevier B.V. All ri...

We prove that in almost all large tournaments, the minimal covering set is the entire set of alternatives. That is, as the number of alternatives gets large, the probability that the minimal covering set of a uniformly chosen random tournament is the entire set of alternatives goes to one. By contrast, it follows from a result of Fisher and Reeves (1995) that the bipartisan set contains about h...

In this paper we study the minimal number τ(S,G) of translates of an arbitrary subset S of a group G needed to cover the group, and related notions of the efficiency of such coverings. We focus mainly on finite subsets in discrete groups, reviewing the classical results in this area, and generalizing them to a much broader context. For example, we show that while the worst-case efficiency when ...

The set covering problem (SCP) is one of representative combinatorial optimization problems, which has many practical applications. The continuous development of mathematical programming has derived a number of impressive heuristic algorithms as well as exact branch-and-bound algorithms, which can solve huge SCP instances of bus, railway and airline crew scheduling problems. We survey heuristic...

We generalize the classical algorithms of Valiant and Haussler for learning conjunctions and disjunctions of Boolean attributes to the problem of learning these functions over arbitrary sets of features; including features that are constructed from the data. The result is a general-purpose learning machine, suitable for practical learning tasks, that we call the Set Covering Machine. We present...

We study in this article polynomial approximation of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant)...