C. K. Wong

A conference key distribution system

Encryption is used in a communication system to safeguard information in the transmitted messages from anyone other than the intended receiver(s). To perform the encryption and decryption the transmitter and receiver(s) ought to have matching encryption and decryption keys. A clever way to generate these keys is to use the public key distribution system invented by Diffie and Hellman. That system, however, admits only one pair of communication stations to share a particular pair of encryption and decryption keys, The public key distribution system is generalized to a conference key distribution system (CKDS) which admits any group of stations to share the same encryption and decryption keys. The analysis reveals two important aspects of any conference key distribution system. One is the multitap resistance, which is a measure of the information security in the communication system. The other is the separation of the problem into two parts: the choice of a suitable symmetric function of the private keys and the choice of a suitable one-way mapping thereof. We have also shown how to use CKDS in connection with public key ciphers and an authorization scheme.

Provably good performance-driven global routing

The authors propose a provably good performance-driven global routing algorithm for both cell-based and building-block design. The approach is based on a new bounded-radius minimum routing tree formulation. The authors first present several heuristics with good performance, based on an analog of Prims minimum spanning tree construction. Next, they give an algorithm which simultaneously minimizes both routing cost and the longest interconnection path, so that both are bounded by small constant factors away from optimal. They also show that geometry helps in routing: in the Manhattan plane, the total wire length for Steiner routing improves to 3/2*(1+(1/ epsilon )) times the optimal Steiner tree cost, while in the Euclidean plane, the total cost is further reduced to (2/ square root 3)*(1+(1/ epsilon )) times optimal. The method generalizes to the case where varying wire length bounds are prescribed for different source-sink paths. Extensive simulations confirm that this approach works well. >

Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees

SummaryGiven a file of N records each of which has k keys, the worst-case analysis for the region and partial region queries in multidimensional binary search trees and balanced quad trees are presented. It is shown that the search algorithms proposed in [1, 3] run in time O(k·N1−1/k) for region queries in both tree structures. For partial region queries with s keys specified, the search algorithms run at most in time O(s·N1−1/k) in both structures.

New algorithms for the rectilinear Steiner tree problem

An approach to constructing the rectilinear Steiner tree (RST) of a given set of points in the plane, starting from a minimum spanning tree (MST), is discussed. The main idea in this approach is to find layouts for the edges of the MST that maximize the overlaps between the layouts, thus minimizing the cost (i.e. wire length) of the resulting rectilinear Steiner tree. Two algorithms for constructing rectilinear Steiner trees from MSTs, which are optimal under the conditions that the layout of each edge of the MST is an L shape or any staircase, respectively, are described. The first algorithm has linear time complexity and the second algorithm has a higher polynomial time complexity. Steiner trees produced by the second algorithm have a property called stability, which allows the rerouting of any segment of the tree, while maintaining the cost of the tree, and without causing overlaps with the rest of the tree. Stability is a desirable property in VLSI global routing applications. >

Bounds for the String Editing Problem

The string editing problem is to determine the distance between two strings as measured by the minimal cost sequence of deletions, insertions, and changes of symbols needed to transform one string into the other. The longest common subsequence problem can be viewed as a special case. Wagner and Fischer proposed an algorithm that runs in time <italic>O</italic>(<italic>nm</italic>), where <italic>n, m</italic> are the lengths of the two strings. In the present paper, it is shown that if the operations on symbols of the strings are restricted to tests of equality, then <italic>O</italic>(<italic>nm</italic>) operations are necessary (and sufficient) to compute the distance.

Worst-Case Analysis of a Placement Algorithm Related to Storage Allocation

In this paper, a discrete minimization problem arising from storage allocation considerations is studied. Owing to the complexity of finding an optimum solution, a heuristic is proposed and its performance is analyzed. The worst-case ratio of the cost by this algorithm to that by the optimum algorithm is shown to lie between 1.03 and 1.04, implying that this algorithm produces a solution within 4 per cent of the optimum. A generalization of this problem to a class of cost functions is also considered. The worst-case ratios for these functions tend, in the limit, to that of the cost function studied by Graham in his classical paper [1].

On some distance problems in fixed orientations

In VLSI design, technology requirements often dictate the use of only two orthogonal orientations, determining both the shape of objects and the distance function, the

Voronoi Diagrams in L1 (L∞) Metrics with 2-Dimensional Storage Applications

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Hierarchical Steiner tree construction in uniform orientations

-metric, to be used for wiring objects. More recent VLSI fabrication technology is capable of creating edges and wires in both the orthogonal and diagonal orientations.We generalize the distance concept to the case where any fixed set of orientations is allowed, and introduce a family of naturally induced metrics, and the subsequent generalization of geometrical concepts. A shortest connection between two points is in this case a path composed of line segments with only the given orientations. We derive optimal solutions for various basic planar distance problems in this setting, such as the computation of a Voronoi diagram, a minimum spanning tree, and the (minimum and maximum) distance between two convex polygons. Many other theoretically interesting and practically relevant problems remain to be solved. In particular, the new famil...

Global routing based on Steiner min-max trees

In this paper we study the problem of scheduling the read/write head movement to handle a batch of