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- Rashid Bin Muhammad
- JNW
- 2007

— This paper presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph. This work considered the idealized unit disk graph model in which nodes are assumed to be connected if, and only if, nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to… (More)

- Rashid Bin Muhammad
- ACM Southeast Regional Conference
- 2006

The Euclidean Steiner tree problem is to find the tree with minimal Euclidean length spanning a given fixed points in the plane, allowing the addition of auxiliary points known as Steiner points. Parallel implementations of local search algorithm are an effective technique to speed up the search for a solution of Steiner tree problem. This technique not… (More)

- Rashid Bin Muhammad
- Seventh ACIS International Conference on Software…
- 2006

This paper presented a parallel local search algorithm for the Steiner tree problem. The main contribution of this work is the O(n<sup>2</sup> log<sup>2</sup> n + log n log(n/ log n)) parallel local search algorithm for computing Steiner tree on the Euclidean plane. The algorithm used proximity structures from computational geometry like, Voronoi diagram,… (More)

- Rashid Bin Muhammad
- Fifth International Conference on Information…
- 2008

This paper presents the computational analysis of the Steiner tree problem on the Server-Client model of computation. In particular, this work analyzes the time delays among server and clients for the parallel Steiner tree algorithm and examines some consequences of time delays on the execution time by considering constant and variable delays.

- Rashid Bin Muhammad
- Seventh IEEE/ACIS International Conference on…
- 2008

This paper presents the computational analysis and simulation of the parallel Steiner tree problem on the client- sever model of computation. In particular, this work analyzes the time delays among server and clients, presents an algorithm for an event-driven simulation of Steiner tree problem on server-client model, and examines some consequences of time… (More)

- Rashid Bin Muhammad
- 21st International Conference on Advanced…
- 2007

This paper presented a fully distributed algorithm to compute a planar subgraph for geo-routing in ad hoc wireless networks. We considered the idealized unit disk graph model in which nodes are assumed to be connected if and only if nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to extract the… (More)

- Rashid Bin Muhammad
- Fourth International Conference on Information…
- 2007

In this paper, we presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph. We considered the idealized unit disk graph model in which nodes are assumed to be connected if and only if nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to… (More)

- Rashid Bin Muhammad
- 22nd International Conference on Advanced…
- 2008

This paper presents the computational analysis of the Steiner tree problem on the server-client model of computation. In particular, this work analyzes the time delays among server and clients for the parallel Steiner tree algorithm and examines some consequences of time delays on the execution time by considering constant and variable delays. The paper… (More)

- Rashid Bin Muhammad
- Fifth International Conference on Information…
- 2008

In this paper, we discuss the problem of assigning transmitting ranges and establishing connectivity in ad hoc wireless networks from the practical perspective. That is, setup a communication links by introducing extraneous nodes to the network in the emergencies. Furthermore, transmitting ranges of nodes must be assigned in such a way that the energy cost… (More)

- Rashid Bin Muhammad
- 22nd International Conference on Advanced…
- 2008

In this paper, we discuss the problem of introducing relay nodes in the given set of original nodes and assigning transmitting ranges to the nodes. The main contribution of this paper is the O(N log N) algorithm to relay nodes to the wireless network and 2-approximation to assign transmitting ranges to nodes (original and relay). The output of the algorithm… (More)