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A novel strategy for constructing the tangent graph, which employs binary search, logarithmic approximation, and half-plane computation methods, is presented. The strategy lends itself well to Very Large Scale Integration (VLSI) implementation, which facilitates high-performance computation.

This brief presents a high speed realization of a residue to binary converter for the {[2.sup.n-1], [2.sup.n], [2.sup.n] + 1} moduli set, which improves upon the best known implementation by almost twice in terms of overall conversion delay. This significant speedup is achieved by using just three extra two input logic gates. Interestingly, by exploiting certain symmetry in operands, we also reduce the hardware requirement of the best known implementation by n - 1 full adders. Finally, the proposed converter eliminates the redundant representation of zero using no extra logic. Index Terms - Modular arithmetic, residue numbers, reverse converters.

In this brief, new architectures are presented for the conversion of residues to binary equivalents in the (2n-1, 2n, 2n + 1) moduli set. Both of the architectures presented are based on a new algorithm, which eliminates a multiplication. In the design of the architectures, speed and cost are considered as the principal factors. The proposed architectures use fewer multipliers and adders of smaller size. A comparison in terms of hardware requirements, delay estimates, and complexity is made to establish the advantages of the proposed design. Index Terms - Modular arithmetic, residue numbers, reverse converters.

Visibility graphs constitute a useful data structure for environment representation in the context of robot path planning. A central element in the construction of the basic visibility graph and its variants is tangent determination. This letter presents new schemes and hardware designs for key elements in tangent construction and identification of obstructed tangents. The designs have been synthesized using Synopsys Design Complier 2001.08-SP1, and results show they are appropriate for development of a cost-effective and efficient visibility graph generation system. Index Terms--Architecture, binary search, logarithmic approximation, navigation systems, robotics, visibility graph.