In this paper we show that the contiguity and linearity of cographs on n vertices are both O(log n). Moreover, we show that this bound is tight for contiguity as there exists a family of cographs on n vertices whose contiguity is Ω(log n). We also provide an Ω(log n/ log log n) lower bound on the maximum linearity of cographs on n vertices. As a by-product of our proofs, we obtain a min-max the...

What is the maximum number of edges of the d-dimensional hypercube, denoted by S d k , that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds for S d k , d 8. These strengthe...

We have seen several randomized approximation algorithms before. Recall that for the MAXCUT and MAX-3SAT problems we proved that choosing any solution uniformly at random gives a constant factor approximation in the expectation. For MAX-CUT the approximation factor was 2. For MAX-3SAT, a random assignment of truth values to a variable satisfies a given clause with probability 78 . In the case o...

In this paper , we prove the first approximate max-flow min-cut theorem for undirected mul t i commodi ty flow. We show tha t for a feasible flow to exist in a mul t icommodi ty problem, it is sufficient t ha t every cut ' s capacity exceeds its demand by a factor of O(logClogD), where C is the sum of all finite capacities and D is the sum of demands . Moreover, our theorem yields an a lgor i t...

The invention and realization of a new technique, software paradigm, or other large piece of work may take place over a period of one or even several decades. It frequently happens that the IP model under which the work was started changes before it is finished—sometimes more than once. This paper explores the development of the Max/MSP/jMax/Pd paradigm, along with some other related developmen...

The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remainsMAX SNP{complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP{complete at the lowest possible degree bounds. Next we study better poly{time approximation of the problem for degree 3 graphs, and improve the previou...

An approximation algorithm for Max Cut is designed and analyzed; its performances are experimentally compared with those of a neural algorithm and of the Goemans and Williamson's algorithm.

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...