Richard C. T. Lee

A New Algorithm for Generating Prime Implicants

This paper describes an algorithm which will generate all the prime implicants of a Boolean function. The algorithm is different from those previously given in the literature, and in many cases it is more efficient. It is proved that the algorithm will find all the prime implicants. The algorithm may possibly generate some nonprime implicants. However, using frequency orderings on literals, the experiments with the algorithm show that it usually generates very few ( possibly none) nonprime implicants. Furthermore, the algorithm may be used to find the minimal sums of a Boolean function. The algorithm is implemented by a computer program in the LISP language.

Some properties of fuzzy logic

In this paper, the fuzzy set ZZadeh (1965)] is viewed as a multivalued logic with a continuum of truth values in the interval Z0, 1]. The concepts of inconsistency, validity, prime implicant and prime implicate are extended to fuzzy logic and various properties of these notions in the context of fuzzy logic are established. It is proved that a formula is valid (inconsistent) in fuzzy logic iff it is valid (inconsistent) in two-valued logic. An algorithm that generates fuzzy prime implicants (implicates) is introduced. A proof of the completeness of this algorithm is also given.

A Heuristic Relaxation Method for Nonlinear Mapping in Cluster Analysis

A relaxation method mapping high-dimensional sample points to low-dimensional sample points is discussed. This method tries to preserve the local interdistance of sample points. Some special heuristics have been introduced to handle the difficulty arising from a large amount of data. Experimental results with handwritten character data and Iris data show that the method runs fast, converges rapidly, and requires a small amount of memory space.

Counting clique trees and computing perfect elimination schemes in parallel

Abstract In a previous result, the authors showed that a clique tree of a chordal graph can be constructed in O(log n ) parallel computing time with O( n 3 ) processors on CRCW PRAM, where n is the number of nodes of the graph. In this paper, it will be shown that this result can be extended in two ways. First, we show that from the parallel clique tree constructing algorithm, we can derive an exact formula of counting clique trees of a labeled connected chordal graph. Next, we show that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 2 ) processors on CREW PRAM once a clique tree of the graph is given. This implies that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 3 ) processors on CRCW PRAM.

Clustering Analysis and Its Applications

Clustering analysis(1–4) is a newly developed computer-oriented data analysis technique. It is a product of many research fields: statistics, computer science, operations research, and pattern recognition. Because of the diverse backgrounds of researchers, clustering analysis has many different names. In biology, clustering analysis is called “taxonomy”.(5,6) In pattern recognition(7–15) it is called “unsupervised learning.” Perhaps the most confusing name of all, the term “classification” sometimes also denotes clustering analysis. Since classification may denote discriminant analysis, which is totally different from clustering analysis, it is perhaps important to distinguish these two terms.

THE SLAB DIVIDING APPROACH TO SOLVE THE EUCLIDEAN P-CENTER PROBLEM

Givenn demand points on the plane, the EuclideanP-Center problem is to findP supply points, such that the longest distance between each demand point and its closest supply point is minimized. The time complexity of the most efficient algorithm, up to now, isO(n2p−1· logn). In this paper, we present an algorithm with time complexityO(n0(√P)).

Voronoi Diagrams of Moving Points in the Plane

In this paper, we consider the dynamic Voronoi diagram problem. In this problem, a given set of planar points are moving and our objective is to find the Voronoi diagram of these moving points at a...

Application of Principal Component Analysis to Multikey Searching

In this paper, we shall introduce a concept widely used by statisticians, the principal component analysis technique. We shall show that this principal component analysis technique can be used to create new keys from a set of old keys. These new keys are very useful in narrowing down the search domain. We shall also show that the projections on the first principal component direction can be viewed as hashing addresses for the best-match searching problem.

Applications of Artificial Intelligence: Relationships between Mass Spectra and Pharmacological Activity of Drugs

The possibility that the mass spectrum and pharmacological activity of a compound may be directly related has been explored with the help of various computer-based pattern-recognition techniques. The relationship appears to hold at least for tranquilizers and sedatives, and compounds with one or the other of these two pharmacological activities can thus be classified from their mass spectra with a high degree of accuracy.

The weighted perfect domination problem and its variants

Abstract A perfect dominating set of a graph G = ( V , E ) is a subset D of V such that every vertex not in D is adjacent to exactly one vertex in D . The perfect domination problem is to find the minimum size of a perfect dominating set of a graph. Suppose moreover that every vertex v ϵ V has a cost c ( v ) and every edge eϵE has a cost c ( e ). The weighted perfect domination problem is to find a perfect dominating set D such that its total cost c ( D ) = ∑{ c ( v ): ϵD } + ∑{ c ( u , v ): u ∉ D , vϵD and ( u , v ) ϵ E } is minimum. We also consider the following three variants of perfect domination. A perfect dominating set. D is called independent (resp. connected, total) if the subgraph 〈 D 〉 induced by D has no edge (resp. is connected, has no isolated vertex). This paper first proves that the three variants of perfect domination are NP-complete for bipartite graphs and chordal graphs, except for the connected perfect domination in chordal graphs. We then present linear-time algorithms for the weighted perfect domination problem and its three variants in block graphs.