How generic language extensions enable ''open-world'' design in Java

By \emph{open--world design} we mean that collaborating classes are so loosely coupled that changes in one class do not propagate to the other classes, and single classes can be isolated and integrated in other contexts. Of course, this is what maintainability and reusability is all about. In the paper, we will demonstrate that in Java even an open--world design of mere attribute access can only be achieved if static safety is sacrificed, and that this conflict is unresolvable \emph{even if the attribute type is fixed}. With generic language extensions such as GJ, which is a generic extension of Java, it is possible to combine static type safety and open--world design. As a consequence, genericity should be viewed as a first--class design feature, because generic language features are preferably applied in many situations in which object--orientedness seems appropriate. We chose Java as the base of the discussion because Java is commonly known and several advanced features of Java aim at a loose coupling of classes. In particular, the paper is intended to make a strong point in favor of generic extensions of Java

Symmetries in logic programs

We investigate the structures and above all, the applications of a class of symmetric groups induced by logic programs. After establishing the relationships between minimal models of logic programs and their simplified forms, and models of their completions, we show that in general when deriving negative information, we can apply the CWA, the GCWA, and the completion procedure directly from some simplified forms of the original logic programs. The least models and the results of SLD-resolution stay invariant for definite logic programs and their simplified forms. The results of SLDNF-resolution, the standard or perfect models stay invariant for hierarchical, stratified logic programs and some of their simplified forms, respectively. We introduce a new proposal to derive negative information termed OCWA, as well as the new concepts of quasi-definite, quasi-hierarchical and quasi-stratified logic programs. We also propose semantics for them

New approximation algorithms for the achromatic number

The achromatic number of a graph is the greatest number of colors in a coloring of the vertices of the graph such that adjacent vertices get distinct colors and for every pair of colors some vertex of the first color and some vertex of the second color are adjacent. The problem of computing this number is NP-complete for general graphs as proved by Yannakakis and Gavril 1980. The problem is also NP-complete for trees, that was proved by Cairnie and Edwards 1997. Chaudhary and Vishwanathan 1997 gave recently a $7$-approximation algorithm for this problem on trees, and an $O(\sqrt{n})$-approximation algorithm for the problem on graphs with girth (length of the shortest cycle) at least six. We present the first $2$-approximation algorithm for the problem on trees. This is a new algorithm based on different ideas than one by Chaudhary and Vishwanathan 1997. We then give a $1.15$-approximation algorithm for the problem on binary trees and a $1.58$-approximation for the problem on trees of constant degree. We show that the algorithms for constant degree trees can be implemented in linear time. We also present the first $O(n^{3/8})$-approximation algorithm for the problem on graphs with girth at least six. Our algorithms are based on an interesting tree partitioning technique. Moreover, we improve the lower bound of Farber {\em et al.} 1986 for the achromatic number of trees with degree bounded by three

Approximation Algorithms for the Achromatic Number

INTRODUCTION A complete coloring of agY3fi G E# is a partition P =#V of the vertices V such that each induced subgedb #, V i P , is an independent set, and, for each pair of distinct sets V i #V j P , the induced subgub V j is not an independent set. Thelarg8W integW m for which G has a completecoloring is called the achromatic number of thegebG and is denoted by ##G#. 404 0196-6774/01 $35.00 2001 Elsevier Science All rigWW reserved The achromatic number was defined and studied by Harary et al. [7] and Harary and Hedetniemi [6].Computing the achromatic number for agG8 eral galb was proved NP-complete by Yannakakis and Gavril [11]. A simple proof of this fact appears in [5]. Bodlaender [1] proved, further, that the problem remains NP-complete even when we limit ourselves to connected gonne that are both intervalgterv and co-g3T3bV The NP-completeness of the achromatic number for trees was established only recently [9]. For gbGFT that are complements of trees th