Class Steiner trees and VLSI-design

Ihler, Edmund; Reich, Gabriele; Widmayer, Peter

doi:10.1016/s0166-218x(98)00090-0

Cited by 41 publications

(29 citation statements)

References 9 publications

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“…A variant of the GMST problem is the less restrictive At-Least GMST (LGMST) problem where more than one node is allowed to be connected from each cluster (Ihler, Reich, and Widmayer, 1999;Dror, Haouari, and Chaouachi, 2000). The GMST problem, as well as the LGMST problem, can further be considered as special cases of the Group Steiner Problem (GSP) introduced by Reich and Widmayer (1989).…”

mentioning

confidence: 99%

Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

Leitner

Raidl

2007

J Heuristics

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mentioning

confidence: 99%

Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem

Leitner

Raidl

2007

J Heuristics

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“…Being a generalized version of the Steiner Tree problem, the Group Steiner Tree (GST) problem is also NP-hard [3]. A general node-weighted Steiner Tree problem is an extension of the classical Steiner Tree problem, where nodes have non-zero cost.…”

Section: Time-complexity and Solution Of Sleep-route Problemmentioning

confidence: 99%

Sleep-Route: Assured Sensing with Aggressively Sleeping Nodes

Sarkar

Rao

Prasad

et al. 2014

2014 IEEE 11th International Conference on Mobile Ad Hoc and Sensor Systems

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Abstract-In this article, we propose an energy-efficient data gathering scheme for wireless sensor network called Sleep-Route, which splits the sensor nodes into two sets -active and dormant (low-power sleep). Only the active set of sensor nodes participate in data collection. The sensing values of the dormant sensor nodes are predicted with the help of an active sensor node. Virtual Sensing Framework (VSF) provides the mechanism to predict the sensing values by exploiting the data correlation among the sensor nodes. If the number of active sensor nodes can be minimized, a lot of energy can be saved. The active nodes' selection must fulfill the following constraints -(i) the set of active nodes are sufficient to predict the sensing values of the dormant nodes, (ii) each active sensor nodes can report their data to the sink node (directly or through some other active node(s)). The goal is to select a minimal number of active sensor nodes so that energy savings can be maximized.The optimal set of active node selection raise a combinatorial optimization problem, which we refer as Sleep-Route problem. We show that Sleep-Route problem is NP-hard. Then, we formulate an integer linear program (ILP) to solve the problem optimally. To solve the problem in polynomial time, we also propose a heuristic algorithm that performs near optimally. I. BACKGROUNDSince Sleep-Route works in conjunction with VSF, we provide an overview of VSF in this section. Every sensor node in a WSN senses a physical parameter at a predefined interval and transmits this data to the sink node. Usually, the data collected from various sensors show correlation among themselves -some sensors are highly correlated while some are less correlated. Let us take the example in Fig. 1, if two sensors a and d are reporting highly correlated data, the data of d can be predicted (with high accuracy) from the data of a, without actually sensing the physical parameter by d. d can be kept dormant and can save energy. VSF proposes to save energy by exploiting this correlation for wireless sensor nodes [8]. This situation can occur when sensors use energy harvesting wherein some nodes harvest energy for a short duration and die after using that energy [6]. To predict the sensor data, a virtual sensor (VS) is created for each physical sensor (PS) at the sink as shown in Fig. 1 collected from the sensors to fine-tune the prediction. In active mode, all the circuits of a sensor node such as microprocessor, radio, sensor, clock, etc., remains switched on. As a result, the sensor node spends higher energy in active mode. On the other hand, most of the circuits of a sensor node remain switched off in dormant state, and the energy consumption is minimal. To perform any operation, a sensor node has to be in active mode and it is imperative that number of active nodes should be minimized. In order to keep the sensor network alive for a longer period, energy consumption of the sensor nodes in the network needs to be balanced over time. Thus, state of the nodes switch between...

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“…Other applications can be found in (Dror et al, 2000;Garg et al, 2000;Myung et al, 1995). Due to its practical and theoretical significance, a lot of research attention has been given to this problem (Chekuri et al, 2006;Dror et al, 2000;Duin et al, 2004;Feremans et al, 2001;Ferreira and Filho 2006;Garg et al, 2000;Houari and Chaouachi, 2006;Ihler et al, 1999;Salazar, 2000;Yang and Gillard, 2000). If     ∪ ⋯ ∪  and we are restricted to select exactly one node per group, the resulting problem becomes the generalized minimum spanning tree problem (GMSTP).…”

Section: Introductionmentioning

confidence: 99%