Search

The concept of rainbow connection number of a graph was introduced by Chartrand et al. in 2008. Inspired by this concept, other concepts on colored version of connectivity in graphs were introduced, such as the monochromatic connection number by Caro and Yuster in 2011, the proper connection number by Borozan et al. in 2012, and the conflict-free connection number by Czap et al. in 2018, as well as some other variants of connection numbers later on. Chakraborty et al. proved that to compute the rainbow connection number of a graph is NP-hard. For a long time, it has been tried to fix the computational complexity for the monochromatic connection number, the proper connection number and the conflict-free connection number of a graph. However, it has not been solved yet. Only the complexity results for the strong version, i.e., the strong proper connection number and the strong conflict-free connection number, of these connection numbers were determined to be NP-hard. In this paper, we prove that to compute each of the monochromatic connection number, the proper connection number and the conflict free connection number for a graph is NP-hard. This solves a long standing problem in this field, asked in many talks of workshops and papers. [ABSTRACT FROM AUTHOR]

In this paper, we propose an algorithm which approximates the Two-Sided Scaffold Filling problem to a performance ratio 1.4 + ε. This is achieved through a deep investigation of the optimal solution structure of Two-Sided Scaffold Filling. We make use of a relevant graph aiming at a solution of a Two-Sided Scaffold Filling instance, and evaluate the optimal solution value by the number of connected components in this graph. We show that an arbitrary optimal solution can be transformed into one whose relevant graph admits connected components that are available to compare with the solution of our algorithm in terms of their values. The performance ratio 1.4 + ε is obtained by comparing the bound of such an optimal solution with the solution of our algorithm. [ABSTRACT FROM AUTHOR]

Injective parametrizations are widely used both in theory and in applications. The injectivity of parameteric curves and surfaces means that there are no self-intersections. Toric surface patch is defined by a set of integer lattice points A and corresponding control points and weights, which includes rational tensor product and triangle Bézier patches as special cases. In 2011, Sottile and Zhu presented a geometric method to check the injectivity of 2D toric surface patches. In this paper, we present an improved algorithm of their method. The complexity of the improved algorithm is reduced from O (n 3) to O (n 2) , where n = # (A). Some examples are shown to illustrate the effectiveness of our algorithm. Moreover, the algorithm is also applied to check the injectivity of parameterization in isogeometric analysis. [ABSTRACT FROM AUTHOR]

Many sorting algorithms have been developed to enhance the performance of important applications from different domains such as commercial commuting, operational research and scientific simulation. In this paper, we propose a new in-place sorting algorithm called OneByOne (OBO) sort. When compared to selection sort and bubble sort algorithms, OBO demonstrated faster run time at different array sizes. OBO also showed nearly equal performance when compared to the insertion sort algorithm. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. The weak rupture degree of G is defined as r w (G) = max { ω (G − X) − | X | − m e (G − X) : ω (G − X) > 1 } , where the maximum is taken over all X , the subset of V (G), ω (G − X) is the number of components in G − X , and m e (G − X) is the size (edge number) of a largest component in G − X. This is an important parameter to quantitatively describe the invulnerability of networks. In this paper, based on a study of relationship between network structure and the weak rupture degree, a polynomial algorithm for computing the weak rupture degree of trees is given. [ABSTRACT FROM AUTHOR]

In order to run a dataflow with as low cost as possible, it is often faced with deciding which data-sets in a data-set sequence should be stored, with the rest regenerated. The Intermediate Data-set Storage problem arises from this situation. The current best algorithm for this problem takes O ( n 4 ) time. In this paper, we present two improved algorithms for this problem, the first of which can achieve a time complexity O ( n 2 ) , the second of which O ( r n ) , where n is the number of data-sets in a dataflow, r is a numerical number which indicates how large it is for the maximum storage cost to be divided by the minimum computation cost in the dataflow. [ABSTRACT FROM AUTHOR]

In this paper we prove that the Minimum Latency Aggregation Scheduling (MLAS) problem in the Signal-to-Interference-Noise-Ratio (SINR) model is APX-hard in the uniform power model. [ABSTRACT FROM AUTHOR]