The maximal f-dependent set problem for planar graphs is in NC

Parallel algorithms for the maximal independent set problem in graphs

In this paper we describe the randomized parallel algorithm proposed by Blelloch et al. [BFS12] to compute a Maximal Independent Set (MIS) of a given graph. We implemented their algorithm as well as the fastest sequential algorithm and compared their performance with different input graphs. Furthermore, we compared the number of rounds in both the sequential and parallel algorithms and present ...

The Degree/Diameter Problem in Maximal Planar Bipartite graphs

The (∆, D) (degree/diameter) problem consists of finding the largest possible number of vertices n among all the graphs with maximum degree ∆ and diameter D. We consider the (∆, D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We prove that for the (∆, 2) problem, the number of vertices is n = ∆ + 2; and for the (∆, 3) problem, n...

The Maximum Independent Set Problem in Planar Graphs

We study the computational complexity of finding a maximum independent set of vertices in a planar graph. In general, this problem is known to be NP-hard. However, under certain restrictions it becomes polynomial-time solvable. We identify a graph parameter to which the complexity of the problem is sensible and produce a number of both negative (intractable) and positive (solvable in polynomial...

The Maximum k-Dependent and f-Dependent Set Problem

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.