In this paper we study the problem of bounding the value of the probability distribution function of a random variable X at E[X] + a where a is a small quantity in comparison with E[X], by means of the second and the fourth moments of X. In this particular context, many classical inequalities yield only trivial bounds. By studying the primal-dual moments-generating conic optimization problems, ...

We prove that given a graph, one can efficiently find a set of no more than m/5.217 + 1 nodes whose removal yields a partial twotree. As an application, we immediately get simple algorithms for several problems, including Max-Cut, Max-2-SAT and Max-2-XSAT. All of these take a record-breaking time of O(2), where m is the number of clauses or edges, while only using polynomial space. Moreover, th...

Max-3-SAT. In this problem, the domain is {0, 1}; a collection of constraint types are disjunctions of the form {xi∨xj ∨xk, xi∨xj ∨xk, xi∨xj ∨xk, . . . , xi∨xj ∨xk, xi∨xj, . . . , xi∨ xj, xi, xi} resulting in total of 14 constraint types. Max-Cut. Here, the domain is again {0, 1}, the collection of constraint types is simply {vi 6= vj}. Intuitively, we have one such constraint for each edge in ...

The security performance problems of broadcast channel with an eavesdropper (BCE) have been studied for many years in the field of communication. Many articles have given the meaningful results. However, almost no consequent of an outer bound on BCE has been given by previous work, especially, no significant results has been given. So this paper proposes and proves an outer bound of BCE by usin...

MAX CUT is the problem of partitioning the vertices of a graph into two sets, maximizing the number of edges joining these sets. Goemans and Williamson gave an algorithm that approximates MAX CUT within a ratio of 0.87856. Their algorithm first uses a semidefinite programming relaxation of MAX CUT that embeds the vertices of the graph on the surface of an n dimensional sphere, and then cuts the...

Many classical partitioning problems in combinatorics ask for a single quantity to be maximized or minimized over a set of partitions of a combinatorial object. For instance, Max Cut asks for the largest bipartite subgraph of a graphG, while Min Bisection asks for the minimum size of a cut into two equal pieces. In judicious partitioning problems, we seek to maximize or minimize a number of qua...

In this paper we summarize recent results on finding tight semidefinite programming relaxations for the Max-Cut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of Max-Cut and in particular we make no assumptions on the edge weights. We present two strengthenings of the well-known semidefinite programming relaxation of Max-Cut studied by Goemans and...

We give a number of improved inapproximability results, including the best up to date explicit approximation thresholds for bounded occurence satis ability problems like MAX2SAT and E2-LIN-2, and the bounded degree graph problems, like MIS, Node Cover, and MAX CUT. We prove also for the rst time inapproximability of the problem of Sorting by Reversals and display an explicit approximation thres...

A simple step and search control strategy for extracting maximum output power from grid connected Variable Speed Wind Energy Conversion System (VSWECS) is implemented in this work. This system consists of a variable speed wind turbine coupled to a Permanent Magnet Synchronous Generator (PMSG) through a gear box, a DC-DC boost converter and a hysteresis current controlled Voltage Source Converte...