Boxicity of a graph G(V,E) is the minimum integer k such that G can be represented as the intersection graph of k-dimensional axis parallel rectangles in R. Equivalently, it is the minimum number of interval graphs on the vertex set V such that the intersection of their edge sets is E. It is known that boxicity cannot be approximated even for graph classes like bipartite, co-bipartite and split...

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cogn...

Is there an NP function that, when given a satissable formula as input, outputs one satisfying assignment uniquely? That is, can a nondeterministic function cull just one satisfying assignment from a possibly exponentially large collection of assignments? We show that if there is such a nondeterministic function, then the polynomial hierarchy collapses to ZPP NP (and thus, in particular, to NP ...

The problem of minimum color sum of a graph is to color the vertices of the graph such that the sum (average) of all assigned colors is minimum. Recently, in [BBH+96], it was shown that in general graphs this problem cannot be approximated within n1 , for any > 0, unless NP = ZPP . In the same paper, a 9=8-approximation algorithm was presented for bipartite graphs. The hardness question for thi...

In the first part, we introduce randomized algorithms as a new notion of efficient algorithms for decision problems. We classify randomized algorithms according to their error probabilities, and define appropriate complexity classes. (RP, coRP, ZPP, BPP, PP). We discuss which classes are realistic proposals for design of probabilistic algorithms. We cover the implementation of randomized algori...

We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of nding the exact value of the chromatic number of a hypergraph is known to be NP -hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r 3 it is impossible to approximate in polynomial time the chromatic number of r-uni...

The MaxClique optimization problem cannot be approximated in polynomial-time within a ratio of n if NP 6= ZPP or within n if P 6= NP (H̊astad, 1999). We investigate the frequency with which approximation algorithms cannot achieve these ratios. Our results include the following for any ǫ > 0. 1. If NP 6= RP, then any polynomial-time approximation algorithm fails to approximate within n on a nonsp...

In transmission electron microscopy (TEM) for biological and polymer samples, it is difficult to image with high contrast, since they are mostly composed of light elements and have similar density. One solution to enhance the contrast is utilization of phase contrast microscopy, which is realized in optical microscopy. Accordingly, many types of phase plates for electron microscopy have been pr...

In this work, we consider contention management in transactional memory in the context of balanced workloads which exhibit better performance potential. Balanced workloads include transactions whose number of exclusive accesses to the shared resources for writes are within a constant fraction of the total accesses (read or writes) to the shared resources. We explore the theoretical performance ...