We study the problem of deploying k base stations in a wireless sensor network such that the maximum shortest hop distance from all the sensor nodes to their designated base stations is minimised. We propose a 2-approximation algorithm for this problem, and prove that a (2− ǫ)-approximation algorithm does not exist unless P = NP holds. The time complexity of our 2-approximation algorithm is O(n...

People have a deep intuition about what has been called the “nature–nurture question.” Some aspects of our behavior feel as though they originate in our genetic makeup, while others feel like the result of our upbringing or our own hard work. The scientific field of behavior genetics attempts to study these differences empirically, either by examining similarities among family members with diff...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebrization of logics [12]. A Priestley-style duality is established between the category of positive modal alg...

DEEP BLUE’s victoryoverKasparov has confirmedtheideas of thegenuineartificialintelligence researchers, but – and that is more important – it has also opened the eyes of the disbelievers. The latter group is now given to understand that (i) scientific progress in mimicking human chess performances can go as far as outperforming the World Champion, and that (ii) progress in one domain may be tran...

Scheduling workflow applications in grid environments is a great challenge, because it is an NP-complete problem. Many heuristic methods have been presented in the literature and most of them deal with a single workflow application at a time. In recent years, there are several heuristic methods proposed to deal with concurrent workflows or online workflows, but they do not work with workflows c...

The problem of distinct value estimation has many applications. Being a critical component of query optimizers in databases, it also has high commercial impact. Many distinct value estimators have been proposed, using various statistical approaches. However, characterizing the errors incurred by these estimators is an open problem: existing analytical approaches are not powerful enough, and ext...

In contrast to the extremal variants of coNP-complete problems, which are frequently DP-complete, many extremal variants of NP-complete problems are in P. We investigate the extremal variants of two NP-complete problems, the extremal colorability problem with restricted degree and the extremal unfrozen non-implicant problem, and show that both of them are DP-complete. As far as we know, no extr...

In this paper, we introduce a new decision problem associated with lattices, named the Exact Length Vector Problem (ELVP), and prove the NP-completeness of ELVP in the ∞ norm. Moreover, we define two variants of ELVP. The one is a binary variant of ELVP, named the Binary Exact Length Vector Problem (BELVP), and is shown to be NPcomplete in any p norm (1 ≤ p ≤ ∞). The other is a nonnegative vari...

This is a survey of work on proof complexity and proof search, as motivated by the P versus NP problem. We discuss propositional proof complexity, Cook’s program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP .