![]() In the geometric model, the cost of an edge is simply the Euclidean distance between its endpoints. In the power model, each edge of the quasi-UDG (or UDG) is associated with a power or energy cost (usually this is the cost required to transmit across the corresponding link in the network), which is commonly assumed to be the Euclidian distance between the endpoints of the edge raised to some power constant β ∈ . For any two points u and v in the set with Euclidean distance | uv|: if | uv| ≤ r then uv is an edge in the graph if | uv| > R then uv is not an edge in the graph and if r < | uv| ≤ R then uv may or may not be an edge in the graph. The points in the set are the vertices of the graph. Definition 1Ī quasi-UDG with parameters r and R ( r and R are positive numbers) over a set of points in the plane is defined as follows. Formally, this model is defined as follows. To combat this problem, a more general network model, the quasi unit-disk graph (quasi-UDG) model, has been recently proposed to capture the nonuniform characteristics of (most) wireless networks. The significant deviation of the UDG model from the real/practical models is substantially limiting the applicability of protocols which are based on UDGs. In practice, however, the UDG model significantly deviates from many real wireless networks, due to many reasons including: multi-path fading, antenna design issues, inaccurate node position estimation, etc. ![]() Examples of these protocols include routing, topology control, distributed information storage/retrieval and a great variety of other applications. So far, many protocols have been based on the idealized unit-disk graph (UDG) network model, where two wireless nodes can directly communicate if and only if their physical distance is within a fixed parameter R. A deep understanding of the structural properties of wireless networks is critical for evaluating the performance of network protocols and improving their designs. The connectivity structures of wireless networks exhibit strong correlations with the physical environment due to the signal transmission model of wireless nodes. We demonstrate the excellent performance of these auxiliary graphs through simulations and show their applications in efficient routing. We present a distributed local algorithm that, given a quasi-UDG, constructs a nearly planar backbone with a constant stretch factor and a bounded degree. We also study the problem of constructing an energy-efficient backbone for a quasi-UDG. We prove that every quasi-UDG has a corresponding grid graph with small balanced separators that captures its connectivity properties. Network separability is a fundamental property leading to efficient network algorithms and fast parallel computation. In this paper, we present results on two important properties of quasi-UDGs: separability and the existence of power efficient spanners. ![]() However, the understanding of the properties of general quasi-UDGs has been very limited, which is impeding the designs of key network protocols and algorithms. A more general network model, the quasi unit-disk graph (quasi-UDG) model, captures much better the characteristics of wireless networks. The significant deviation of the UDG model from many real wireless networks is substantially limiting the applicability of such protocols. Many protocols for wireless networks-routing, topology control, information storage/retrieval and numerous other applications-have been based on the idealized unit-disk graph (UDG) network model. Is allowed), both of our algorithms are almost optimal.A deep understanding of the structural properties of wireless networks is critical for evaluating the performance of network protocols and improving their designs. The $\Omega(n \log n)$-time lower bound of the problem (even when approximation Download a PDF of the paper titled Near-Optimal Algorithms for Shortest Paths in Weighted Unit-Disk Graphs, by Haitao Wang and 1 other authors Download PDF Abstract: We revisit a classical graph-theoretic problem, the \textit)))$ time. ![]()
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