This paper discusses an approach for object detection and classification. Object detection approaches find the object or objects of the real world present either in a digital image or a video, where the object can belong to any class of objects. Humans can detect the objects present in an image or video quite easily but it is not so easy to do the same by machine, for this, it is necessary to m...

The Euclidean Steiner tree problem is solved by finding the tree with minimal Euclidean length spanning a set of fixed vertices in the plane, while allowing for the addition of auxiliary vertices (Steiner vertices). Steiner trees are widely used to design real-world structures like highways and oil pipelines. Unfortunately, the Euclidean Steiner Tree Problem has shown to be NP-Hard, meaning the...

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimal possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the metric space. Du et al. (1993) conjectured that the Steiner ratio on a normed plan...

Many multicast routing algorithms have been suggested in the past as multicast communication emerges as one of the important services in communications networks. Many algorithms aim at the Steiner tree model because the Steiner tree is thought to provide the optimal multicast route by minimizing the sum of the link costs. The concept of cost in network routing can apply to various measures of n...

We introduce and study a new Steiner tree problem variation called the bursty Steiner tree problem where new nodes arrive into bursts. This is an online problem which becomes the well-known online Steiner tree problem if the number of nodes in each burst is exactly one and becomes the classical Steiner tree problem if all the nodes that need to be connected appear in a single burst. In undirect...

Given a complete graph G = (V,E) with a metric cost function c : E → R and two vertex subsets R ⊂ V and R ⊆ R, a partial-terminal Steiner tree is a Steiner tree which contains all the vertices in R such that all the vertices in R are leaves. The partial-terminal Steiner tree problem (PTSTP) is to find a partial-terminal Steiner tree with the minimum cost. The problem has been shown to be NP-har...

We study global routing of multiterminal nets. We propose a new global router: each step consists of finding a tree, called a Steiner min-max tree, that is a Steiner tree with maximum-weight edge minimized (real vertices represent channels containing terminals of a net, Steiner vertices represent intermediate channels, and weights correspond to densities). We propose an 0 (min { e loglog e , n*...

A-Tree is a rectilinear Steiner tree in which every sink is connected to a driver by a shortest length path, while simultaneously minimizing total wire length. This paper presents a polynomial approximation algorithm for the generalized version of A-Tree problem with upper-bounded delays along each path from the driver to the sinks and with restrictions on the number of Steiner nodes. We refer ...

The node-weighted Steiner tree problem is a variation of classical Steiner minimum tree problem. Given a graph G = (V,E) with node weight function C : V → R and a subset X of V , the node-weighted Steiner tree problem is to find a Steiner tree for the set X such that its total weight is minimum. In this paper, we study this problem in unit disk graphs and present a (1+ε)-approximation algorithm...

The concept of pendant tree-connectivity was introduced by Hager in 1985. For a graph G = (V,E) and a set S ⊆ V (G) of at least two vertices, an S-Steiner tree or a Steiner tree connecting S (or simply, an S-tree) is a subgraph T = (V ′, E ′) of G that is a tree with S ⊆ V ′. For an S-Steiner tree, if the degree of each vertex in S is equal to one, then this tree is called a pendant S-Steiner t...