A graph G is locally irregular if adjacent vertices of G have different degrees. A k-edge colouring φ of G is locally irregular if each of the k colours of φ induces a locally irregular subgraph of G. The irregular chromatic index χirr(G) of G is the least number of colours used by a locally irregular edge colouring ofG (if any). We show that determining whether χirr(G) = 2 is NP-complete, even...

We introduce and study online balanced coloring games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are introduced two at the time, in a random order. For each pair of edges, Painter immediately and irrevocably chooses one of the two possibilities to color one of them red and the other one blue. His goal is to avoid crea...

1 CONTENTS 2 Figure 1: A partitioned 2D irregular mesh of an airfoil. The shading of a mesh element indicates the processor to which i t is mapped. 0.1 Introduction Algorithms that nd good partitionings of unstructured and irregular graphs are critical for the eecient execution of scientiic simulations on high performance parallel computers. In these simulations, computation is performed iterat...

An equation for photons containing a frequency drift term modeling the Doppler effects and an emission absorption coefficient is considered. On the one hand, this frequency drift term involves a coefficient κ relative to the fluid velocity with which the photons interact. This coefficient may vanish, leading to numerical difficulties. On the second hand, the emission absorption σ is known to be...

Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. A new domain mapping algorithm is presented that extends recent work in which ideas from spectral graph theory have been applied to this problem. The generalization of spectral graph bisection involves a novel use of mul...

Modern High Performance Computing (HPC) clusters are composed of hundred of nodes integrating multicore processors with advanced cache hierarchies. These systems can reach several petaflops of peak performance, but are optimized for floating point intensive applications, and regular, localizable data structures. The network interconnection of these systems is optimized for bulk, synchronous tra...

The Bounded Irregular Pyramid (BIP) is a hierarchical structure for image representation whose aim is to combine concepts from regular and irregular pyramids. The data structure is a combination of the simplest regular and irregular structures: the 2× 2/4 regular one and the simple graph representation. However, simple graphs only take into account adjacency relationships, being unable to corre...

Given a connected graph $$G = (V, E)$$ , we seek to partition the vertex set V into k non-empty parts such that subgraph induced by each part is connected, and maximally balanced in way maximum cardinality of these minimized. We refer this problem as min-max denote it -BGP. The vertex-weighted version on trees has been studied since about four decades ago, which admits linear time exact algorit...