Steiner trees

This paper addresses the optimal cable layout design of a collector system in a large-scale wind farm. The objective is the minimization of total trenching length which is the sum of lengths of all branches of the collector system tree. A graph-theoretic minimum spanning tree algorithm has been used as a starting algorithm, and improvements and modifications have been proposed to cater to the constraints and characteristics of a wind farm collector system. The contribution of this paper is three-fold. First, an algorithm has been proposed to further improve the results of the minimum spanning tree algorithm by creating external splice locations separate from the wind turbine locations in computing the cable layout configuration. Second, an algorithm has been proposed to compute the minimum trenching length layout configuration under the constraint of a prespecified maximum number of turbines connected to a feeder cable. Third, an algorithm has been developed to automatically compute the direction and magnitude of power flow on the different cables and to assign cable sizes accordingly.

A minimum degree spanning tree of a graph G is a spanning tree of G whose maximum degree is minimum among all spanning trees of G. The minimum degree spanning tree problem (MDST) is to construct such a spanning tree of a graph. In this paper, we propose a polynomial-time algorithm for solving the MDST problem on series-parallel graphs. Our algorithm runs in linear time for series-parallel graphs with small degrees. By applying this algorithm, we also give an approximation algorithm for solving the minimum edge-ranking spanning tree problem on series-parallel graphs.

The Steiner problem leads to solutions in several scientific and business applications. Computer networks routing and electronic integrated circuits are few examples of it. Assuming some points in the Euclidean plane, we can construct a minimum spanning tree connecting these (terminal) nodes. It is possible to add some extra points (Steiner Points) in order to decrease the length of this tree, which would in turn lead to Euclidean Steiner Minimal Tree (ESMT). This problem is considered as a NP-hard problem, as it may contain some nodes that are not in the set of given nodes. Assuming a simple polygon with vertices and terminals in it, we try to find an Euclidean Steiner minimal tree connecting all these terminals in. In this paper, we propose a new solution based on the straight skeleton of a simple polygon for finding Euclidean Steiner tree of any number of terminals, in a given simple polygon.

Using multiple datacenters allows for higher availability, load balancing and reduced latency to customers of cloud services. To distribute multiple copies of data, cloud providers depend on inter-datacenter WANs that ought to be used efficiently considering their limited capacity and the ever-increasing data demands. In this paper, we focus on applications that transfer objects from one datacenter to several datacenters over dedicated inter-datacenter networks. We present DCCast, a centralized Point to Multi-Point (P2MP) algorithm that uses forwarding trees to efficiently deliver an object from a source datacenter to required destination datacenters. With low computational overhead, DCCast selects forwarding trees that minimize bandwidth usage and balance load across all links. With simulation experiments on Google’s GScale network, we show that DCCast can reduce total bandwidth usage and tail Transfer Completion Times (TCT) by up to 50% compared to delivering the same objects via independent point-to-point (P2P) transfers.

Group communication has become increasingly important in mobile ad hoc networks (MANET). Current multicast routing protocols in MANET have a large overhead due to the dynamic network topology. To overcome this problem, there is a recent shift towards stateless multicast in small groups. We introduce a small group multicast scheme, based on packet encapsulation, which uses a novel packet distribution tree construction algorithms for efficient data delivery. The tree is constructed with the goal of minimizing the ...

The high-level contribution of this paper is to establish benchmarks for the minimum hop count per source-receiver path and the minimum number of edges per tree for multicast routing in mobile ad hoc networks (MANETs) under different mobility models. In this pursuit, we explore the tradeoffs between these two routing strategies with respect to hop count, number of edges and lifetime per multicast tree with respect to the Random Waypoint, City Section and Manhattan mobility models. We employ the Breadth First Search algorithm and the Minimum Steiner Tree heuristic for determining a sequence of minimum hop and minimum edge trees respectively. While both the minimum hop and minimum edge trees exist for a relatively longer time under the Manhattan mobility model; the number of edges per tree and the hop count per source-receiver path are relatively low under the Random Waypoint model. For all the three mobility models, the minimum edge trees have a longer lifetime compared to the minimum hop trees and the difference in lifetime increases with increase in network density and/or the multicast group size. Multicast trees determined under the City Section model incur fewer edges and lower hop count compared to the Manhattan mobility model.

Recent advances in technology have led to robots with communication capability. These networked robots can provide a communication substrate by establishing a wireless network backbone. The wireless network is useful in many settings, such as urban search and rescue, fire fighting, military operations, and disaster response. Given a set of clients, such as fire-fighters, the network robots can establish a network backbone guaranteeing that all clients are connected. A fundamental problem is what is the minimal number of robots and where should they be placed to establish a network without any partition. In this work, we investigate the problem of calculating the position of the mobile networked robots so they can establish a communication backbone for a set of clients. We present a graph-based algorithm in order to calculate the position of the networked robots. The methodology was thoroughly evaluated through numerous trials considering different conditions, providing statistical examination of the final results. We compare our results with the Minimum Spanning Tree algorithm, which is useful as a standard algorithm for comparison. Our results show that our approach is correct and uses fewer robots.

A minimum degree spanning tree of a graph G is a spanning tree of G whose maximum degree is minimum among all spanning trees of G. The minimum degree spanning tree problem (MDST) is to construct such a spanning tree of a graph. In this paper, we propose a polynomial-time algorithm for solving the MDST problem on series-parallel graphs. Our algorithm runs in linear time for series-parallel graphs with small degrees. By applying this algorithm, we also give an approximation algorithm for solving the minimum edge-ranking spanning tree problem on series-parallel graphs.

A tool capable of synthesizing the symbolic layout of a CMOS cell from its circuit descriptions is presented. The synthesis process is guided by topological constraints on pin and transistor positions, maximum lengths of poly and diffusion wires, and the specification of a preferred layer for each electrical node. The optimization criteria, take into account cell area and aspect ratio, wire length, capacitance to the substrate, and contact and via minimization. The novel placement strategy includes transistor clustering into regions, global region placement by linear ordering, and two-dimensional local transistor placement. The routing combines Steiner trees and Lee algorithms. The program is fast and has been thoroughly tested on small and medium-sized cells

A minimum degree spanning tree of a graph G is a spanning tree of G whose maximum degree is minimum among all spanning trees of G. The minimum degree spanning tree problem (MDST) is to construct such a spanning tree of a graph. In this paper, we propose a polynomial-time algorithm for solving the MDST problem on series-parallel graphs. Our algorithm runs in linear time for series-parallel graphs with small degrees. By applying this algorithm, we also give an approximation algorithm for solving the minimum edge-ranking spanning tree problem on series-parallel graphs.

We consider the Connected Facility Location problem. We are given a graph G=(V, E) with cost ce on edge e, a set of facilities F⊆ V, and a set of demands D⊆ V. We are also given a parameter M≥ 1. A solution opens some facilities, say F, assigns each demand j to an ...

We consider the Connected Facility Location problem. We are given a graph G=(V, E) with cost ce on edge e, a set of facilities F⊆ V, and a set of demands D⊆ V. We are also given a parameter M≥ 1. A solution opens some facilities, say F, assigns each demand j to an ...