By Sandor P. Fekete
This e-book constitutes the reviewed lawsuits of the Fourth foreign Workshop on Algorithmic points of instant Sensor Networks, ALGOSENSORS 2008, held in Reykjavik, Iceland, Wroclaw, Poland, July 12, 2008. The workshops aimed toward bringing jointly study contributions relating to varied algorithmic and complexity-theoretic points of instant sensor networks. the themes comprise yet will not be restricted to optimization difficulties, noise and likelihood, robots and excursions.
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Extra info for Algorithmic Aspects of Wireless Sensor Networks: Fourth International Workshop, Algosensors 2008, Reykjavik, Iceland, July 2008. Revised Selected Pape ... Computer Science Computer Communication N)
Unfortunately, in general, integer linear programming is NP-Hard. Fortunately, the special structure of our problem admits a rather eﬃcient (polynomial time) solution, by a transformation to a shortest path problem. In particular, all the constraints in our problem have the form of a diﬀerence constraint. We explain the reduction to the shortest path problem, using an example. Consider the example shown in Figure 3, with 7 targets and 3 sensors. The true target positions are shown as solid circles.
Research in sensor networks has seen a lot of work in tracking multiple targets [14,15,16,17,18,19,20,21] and almost every piece of work assumes that the number of targets in the network is known. Our work is closely related to [5,6] in terms of deriving fundamental limits for tracking and counting targets using a minimal sensing model. These papers use a binary sensing model, which has also been considered by [1,2,3,4]. Counting sensor model is similar to the binary model in terms of minimal sensing, instead of transmitting a bit of information, counting sensors transmit an integer representing the number of targets in their Target Counting under Minimal Sensing: Complexity and Approximations 41 range.
Gandhi, R. Kumar, and S. Suri The Bellman-Ford shortest path algorithm, in fact, has an interesting property: the algorithm minimizes the maximum diﬀerence between the diﬀerence variables. In other words, the algorithm not only ﬁnds a feasible assignment of variables, but actually ﬁnds an assignment satisfying min max 1≤i≤2n,1≤j≤2n |zi − zj | In our setting, the maximum diﬀerence is between the variables z2n and z1 (Equation 1). But z2n − z1 equals the total number of targets in the solution, and so our algorithm ﬁnds a feasible solution with the least possible number of targets consistent with the sensors’ counts.
Algorithmic Aspects of Wireless Sensor Networks: Fourth International Workshop, Algosensors 2008, Reykjavik, Iceland, July 2008. Revised Selected Pape ... Computer Science Computer Communication N) by Sandor P. Fekete