Author
Sandra M. Hedetniemi
Bio: Sandra M. Hedetniemi is an academic researcher from Clemson University. The author has contributed to research in topics: Dominating set & Vertex (geometry). The author has an hindex of 17, co-authored 36 publications receiving 2716 citations.
Papers
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TL;DR: Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network as discussed by the authors, and the results that have been obtained on these and related problems.
Abstract: Gossiping and broadcasting are two problems of information dissemination described for a group of individuals connected by a communication network. In gossiping every person in the network knows a unique item of information and needs to communicate it to everyone else. In broadcasting one individual has an item of information which needs to be communicated to everyone else. We review the results that have been obtained on these and related problems.
1,191 citations
TL;DR: The graph theoretic properties of this variant of the domination number of a graph G, a function f : V→{0,1,2} satisfying the condition that every vertex u is adjacent to at least one vertex v for which f(v)=2, are studied.
456 citations
TL;DR: It is shown that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs and a linear algorithm is given to solve the PDS for trees.
Abstract: The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graphs. We consider the graph theoretical representation of this problem as a variation of the dominating set problem and define a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph G is the power domination number $\gamma_P(G)$. We show that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs. On the other hand, we give a linear algorithm to solve the PDS for trees. In addition, we investigate theoretical properties of $\gamma_P(T)$ in trees T.
327 citations
TL;DR: This paper shows that approximating MAPs with a constant ratio bound is also NP-hard, and applies to networks with constrained in-degree and out-degree, applies to randomized approximation, and even applies if the ratio bound, instead of being constant, is allowed to be a polynomial function of various aspects of the network topology.
118 citations
TL;DR: For undirected path graphs, the problem remains NP-complete as discussed by the authors, and it was shown that the problem is not solvable in linear time for any tree, even in the case of trees.
Abstract: A set of vertices D is a dominating set for a graph $G = (V,E)$ if every vertex not in D is adjacent to a vertex in D. A set of vertices is a total dominating set if every vertex in V is adjacent to a vertex in D. Cockayne, Goodman and Hedetniemi presented a linear time algorithm to determine minimum dominating sets for trees. Booth and Johnson established the NP-completeness of the problem for undirected path graphs. This paper presents a linear time algorithm to determine minimum total dominating sets of a tree and shows that for undirected path graphs the problem remains NP-complete.
106 citations
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TL;DR: The concept of sensor networks which has been made viable by the convergence of micro-electro-mechanical systems technology, wireless communications and digital electronics is described.
17,936 citations
TL;DR: The current state of the art of sensor networks is captured in this article, where solutions are discussed under their related protocol stack layer sections.
Abstract: The advancement in wireless communications and electronics has enabled the development of low-cost sensor networks. The sensor networks can be used for various application areas (e.g., health, military, home). For different application areas, there are different technical issues that researchers are currently resolving. The current state of the art of sensor networks is captured in this article, where solutions are discussed under their related protocol stack layer sections. This article also points out the open research issues and intends to spark new interests and developments in this field.
14,048 citations
TL;DR: A survey of state-of-the-art routing techniques in WSNs is presented and the design trade-offs between energy and communication overhead savings in every routing paradigm are studied.
Abstract: Wireless sensor networks consist of small nodes with sensing, computation, and wireless communications capabilities. Many routing, power management, and data dissemination protocols have been specifically designed for WSNs where energy awareness is an essential design issue. Routing protocols in WSNs might differ depending on the application and network architecture. In this article we present a survey of state-of-the-art routing techniques in WSNs. We first outline the design challenges for routing protocols in WSNs followed by a comprehensive survey of routing techniques. Overall, the routing techniques are classified into three categories based on the underlying network structure: flit, hierarchical, and location-based routing. Furthermore, these protocols can be classified into multipath-based, query-based, negotiation-based, QoS-based, and coherent-based depending on the protocol operation. We study the design trade-offs between energy and communication overhead savings in every routing paradigm. We also highlight the advantages and performance issues of each routing technique. The article concludes with possible future research areas.
4,701 citations
01 May 2005
TL;DR: The three main categories explored in this paper are data-centric, hierarchical and location-based; each routing protocol is described and discussed under the appropriate category.
Abstract: Recent advances in wireless sensor networks have led to many new protocols specifically designed for sensor networks where energy awareness is an essential consideration. Most of the attention, however, has been given to the routing protocols since they might differ depending on the application and network architecture. This paper surveys recent routing protocols for sensor networks and presents a classification for the various approaches pursued. The three main categories explored in this paper are data-centric, hierarchical and location-based. Each routing protocol is described and discussed under the appropriate category. Moreover, protocols using contemporary methodologies such as network flow and quality of service modeling are also discussed. The paper concludes with open research issues. � 2003 Elsevier B.V. All rights reserved.
3,573 citations
TL;DR: This work analyzes the averaging problem under the gossip constraint for an arbitrary network graph, and finds that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm.
Abstract: Motivated by applications to sensor, peer-to-peer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of "gossip" algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the so-called Preferential Connectivity (PC) model.
2,634 citations