In a peer-to-peer (P2P) network, broadcast is a fundamental service for many operations. However, it is not trivial for an activated peer, who has received a broadcast message, to find a non-activated peer in P2P networks. In past years, it had proposed to explicitly build a spanning tree so that each peer can forward the broadcast message to its children along the edges on the tree, and aggreg...

The edges of an image define the image boundary. When the image is noisy, it does not become easy to identify the edges. Therefore, a method requests to be developed that can identify edges clearly in a noisy image. Many methods have been proposed earlier using filters, transforms and wavelets with Ant colony optimization (ACO) that detect edges. We here used ACO for edge detection of noisy ima...

The congested clique is a synchronous, message-passing model of distributed computing in which each computational unit (node) in each round can send message of O(log n) bits to each other node of the network, where n is the number of nodes. This model has been considered under two extreme scanarios: unicast or broadcast. In the unicast model, a node can send (possibly) different message to each...

We study dynamic matching problems in graphs among agents with preferences. Agents and/or edges of the graph arrive and depart iteratively over time. The goal is to maintain matchings that are favorable to the agent population and stable over time. More formally, we strive to keep a small unpopularity factor by making only a small amortized number of changes to the matching per round. Our main ...

The Padmakar-Ivan (PI) index is a first-generation topological index (TI) based on sums over all edges between numbers of edges closer to one endpoint and numbers of edges closer to the other endpoint. Edges at equal distances from the two endpoints are ignored. An analogous definition is valid for the Wiener index W, with the difference that sums are replaced by products. A few other TIs are d...

We consider the well-known vertex coloring problem: given a graph G, find a coloring of the vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree∆ can be colored with ∆+1 colors, and distributed algorithms that find a (∆+1)coloring in a logarithmic number of communication rounds, with high probability, are known since more than a dec...

We consider the well-known vertex coloring problem: given a graph G, find a coloring of the vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree ∆ can be colored with ∆+1 colors, and distributed algorithms that find a (∆+1)coloring in a logarithmic number of communication rounds, with high probability, are known since more than a de...

Multi-edge trees as introduced in a recent paper of Dziemiańczuk are plane trees where multiple edges are allowed. We first show that d-ary multi-edge trees where the out-degrees are bounded by d are in bijection with classical d-ary trees. This allows us to analyse parameters such as the height. The main part of this paper is concerned with multi-edge trees counted by their number of edges. Th...

A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of edges incident to to a same vertex. A rooted trivalent diagram is a trivalent diagram with a distinguished edge, its root. We shall describe and analyze an a...