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...

An Sq[t,k,v] q-Steiner system is a collection of k-dimensional subspaces of the v-dimensional vector space Fq over the finite field Fq with q elements, called blocks, such that each t-dimensional subspace of Fq is contained in exactly one block. The smallest admissible parameters for which a q-Steiner system could exist is S2[2,3,7]. Up to now the issue whether q-Steiner systems with these para...

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*...

Given a directed graph G and a list (s1, t1), . . . , (sk, tk) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of G that contains a directed si → ti path for every 1 ≤ i ≤ k. The special case Directed Steiner Tree (when we ask for paths from a root r to terminals t1, . . . , tk) is known to be fixed-parameter tractable parameterized by the number of term...

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 advances in VLSI technology have led to complex and larger circuits. As the circuits become complex and large, the amount of time required for the design of such circuits increases. The people in the VLSI industry are looking for faster EDA (Electronic Design Automation) tools so as to reduce the design time. Routing is a phase in the design (physical design) of electronic circuits, wherein...

Let Fn q be a vector space of dimension n over the finite field Fq . A q-analog of a Steiner system (also known as a q-Steiner system), denoted Sq(t,k,n), is a set S of k-dimensional subspaces of Fn q such that each t-dimensional subspace of Fn q is contained in exactly one element of S . Presently, q-Steiner systems are known only for t = 1, and in the trivial cases t = k and k= n. In this pap...

We describe improvements to Smith’s branch-and-bound (B&B) algorithm for the Euclidean Steiner problem in IR. Nodes in the B&B tree correspond to full Steiner topologies associated with a subset of the terminal nodes, and branching is accomplished by “merging” a new terminal node with each edge in the current Steiner tree. For a given topology we use a conic formulation for the problem of locat...

We prove that a partial Steiner triple system 8 of order n can be embedded in a Steiner triple system T of any given admissible order greater than 4w. Furthermore, if G(S), the missing-edge graph of S, has the property that A(G)<ri(n + l)l and \E(G)\ then # can be embedded in a Steiner triple system of order 2n +1, provided that 2w +1 is admissible. We also prove that if there is a partial Stei...