An irregular assignment is a k -labeling of the edges : {1, 2, , } f E k → ... such that the vertex weights (label sums of edges incident with the vertex) are different for all vertices of G . The smallest k for which there is an irregular assignment is the irregularity strength. The notion of irregularity strength was introduced by Chartrand et al. [8] and studied by numerous authors, see [6,1...

In [2, 3, 20, 21] the authors explored a construction to produce multiresolutions from given subdivisions. Certain assumptions carried through that work, two of which we wish to challenge: (1) that multiresolutions for irregular meshes have to be constructed on the fly rather than being prepared beforehand and (2) that the connectivity graph of the coarse mesh would have to be a subgraph of the...

A graph G is locally irregular if every two adjacent vertices of G have different degrees. A locally irregular decomposition of G is a partition E1, ..., Ek of E(G) such that each G[Ei] is locally irregular. Not all graphs admit locally irregular decompositions, but for those who are decomposable, in that sense, it was conjectured by Baudon, Bensmail, Przyby lo and Woźniak that they decompose i...

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The two most important tools in GSP are the graph shift operator (GSO), which is a sparse matrix accounting for the topology of the graph, and the graph Fourier ...

We present a technique for representing bounded-degree planar graphs succinctly while permitting I/O-efficient path traversal. To represent a graph G on N vertices, each with an associated key of q = O(lgN) bits, we use Nq +O(N) + o(Nq) bits. Using this representation, a path of length K can be traversed with O(K/ lgB) I/Os, where B is the disk block size. Our structure may be adapted to repres...

In this paper, we explore the limits of graphics processors (GPUs) for general purpose parallel computing by studying problems that require highly irregular data access patterns: parallel graph algorithms for list ranking and connected components. Such graph problems represent a worst case scenario for coalescing parallel memory accesses on GPUs which is critical for good GPU performance. Our e...

The space-time scan statistic is a widely-used method for cluster detection in which both the geographic locations and the temporal length of the cluster are unknown. It relies on a cylinder scanning window in which the base represents geographic locations and the height represents the time component, simultaneously. Due to the strict shape of the scanning window, different geometries and graph...