As more processing cores are added to embedded systems processors, the relationships between cores and memories have more influence on the energy consumption of the processor. In this paper, we conduct fundamental research to explore the effects of memory sharing on energy in a multicore processor. We study the Memory Arrangement (MA) Problem. We prove that the general case of MA is NP-complete...

We revisit the d-dimensional arrangement problem and analyze the performance ratios of previously proposed algorithms based on the linear arrangement problem with d-dimensional cost. The two problems are related via space-filling curves and recursive balanced bipartitioning. We prove that the worst-case ratio of the optimum solutions of these problems is Θ(log n), where n is the number of verti...

Let A be a finite real linear hyperplane arrangement in three dimensions. Suppose further that all the regions of A are isometric. We prove that A is necessarily a Coxeter arrangement. As it is well known that the regions of a Coxeter arrangement are isometric, this characterizes three-dimensional Coxeter arrangements precisely as those arrangements with isometric regions. It is an open questio...

In this note we study modules of derivations on collections of linear subspaces in a finite dimensional vector space. The central aim is to generalize the notion of freeness from hyperplane arrangements to subspace arrangements. We call this generalization ‘derivation radical’. We classify all coordinate subspace arrangements that are derivation radical and show that certain subspace arrangemen...

A linear arrangement of BODIPY dimers and trimers was transformed into boron-bridged box, ladder and cage structures on treatment with spacer units possessing multiple diol moieties.

We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in ...

4 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that 5 each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing 6 number c̃r(G) of a graph G is the minimum number of pairwise crossings of edges in 7 a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing 8 number, including its computational complexity and i...