We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where they are published, keyword similarity, citations, etc. As such, graphs with multiple edges is a more accurate model to describe similarities between objects. E...

This paper deals with weighted set systems (V, E , q), where V is a set of indices, E ⊂ 2 and the weight q is a nonnegative integer function on E . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V, E , q) is...

A pseudo-triangulation on a closed surface without loops is a graph embedded on the surface so that each face is triangular and may have multiple edges, but no lo $0$ps. We shall establish a theory of diagonal flips in those pseudotriangulations. Our theory will work in parallel to that for simple triangulations basically, but it will present more concrete theorems than the latter.

A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops, graphs with multiple edges (with up to m duplications of each edge), directed graphs, hypergraphs, and k-uniform hypergraphs.

The on-line shortest path problem is considered under partial monitoring scenarios. At each round, a decision maker has to choose a path between two distinguished vertices of a weighted directed acyclic graph whose edge weights can change in an arbitrary (adversarial) way such that the loss of the chosen path (defined as the sum of the weights of its composing edges) be small. In the multi-arme...

The possibility of jet-installation noise reduction has been experimentally demonstrated using a flat-plate fitted with flow permeable metal foam at the trailing-edge. Tests were conducted for single-stream cold subsonic jets round nozzle adjacent to wide range velocities (M=0.3?0.9) in an anechoic chamber. Thorough investigations far-field various polar angles carried out demonstrate regions r...

For a fixed integer r, consider the following random process. At each round, one is presentedwith r random edges from the edge set of the complete graph on n vertices, and is asked to chooseone of them. The selected edges are collected into a graph, which thus grows at the rate of oneedge per round. This is a natural generalization of what is known in the literature as an Achlio...

The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress multi-round Fibonacci heap operations to one round to save running time relative to Dijkstra’s algorithm using Fibonacci heap. The time complexity of the algorithm ...

The graphs we shall consider are topological graphs that is they lie in R3 and each edge is homeomorphic to [0, 1]. If a graph is simple, that is it has no loops or multiple edges, then each edge may be taken to be a straight line joining the two vertices at the ends of the edge. A function is k-to-1 if each point in the codomain has precisely k preimages in the domain. Given two graphs G and H...

A k-tree is a chordal graph with no (k + 2)-clique. An l-treepartition of a graph G is a vertex partition of G into ‘bags’, such that contracting each bag to a single vertex gives an l-tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k ≥ l ≥ 0, every k-tree has an l-tree-partition in which every bag induces a connected ⌊k/(l + 1)⌋-tree. An analogo...