Abstract
Our natural world is an environment that is highly changes may impact lives on a large scale, such as those caused by a Tsunami, global warming, or global dimming phenomena. Monitoring technologies have improved tremendously over the years in the hope of predicting such events. The manmade world today is also highly complex, and has become increasingly sophisticated. In the same spirit as monitoring systems for the natural world that save lives, technology has also made it possible to monitor structural stress and instabilities within buildings. Target tracking systems (Wong, 2004) using acoustics, passive infra-red, and even other modes, such as chemical compound analysis, are capable of warning against possible attacks by terrorists on our civilized world.
Key Terms in this Chapter
Combinatorics: A branch of mathematics that is concerned with selection, arrangement, and operation of elements in a set. It is sometimes also referred to as the science of counting.
k-Connected Network: A network is k-connected if all nodes in the network remain connected to each other when k nodes are removed (or switched to the Sleep Mode, in our context).
Connected Dominating Set: A dominating set; any two nodes in the set can communicate, possibly through other nodes via multihop broadcasting.
Dominating Set: A subset of network nodes in which each node is either in this subset or is a neighbour of a node in this subset.
Forwarding Set: The set of nodes in the routing table of a node in which information or data packets are forwarded to.
Lonely Node Problem: The lonely node problem happens when a network node wakes up to find no other communicable neighbouring nodes.
k-Neighbour Connected Network: A k-neighbour connected network is one where all nodes have at least k neighbouring nodes for communication.
k-Covered Area: Given a finite number of sensors deployed, a network area is k-covered if at any instant in time, k sensors are in the Awake Mode to monitor that area.
Cyclic Symmetric Block Design: A combinatorial arrangement solution that imposes a time-shifted pre-determined wake-up schedule onto the nodes in a network, so that there is/are always overlap(s) between any two schedules in the design.
Asymptotic k-Covered Area: Assuming that there are an infinite number of sensors deployed, a network area is Asymptotic k-covered if at any instant in time, k sensors are in the Awake Mode to monitor that area.