Sumiyasu Yamamoto

Balanced arrays of strength 2l and balanced fractional 2 m factorial designs

SummaryA connection between a balanced fractional 2m factorial design of resolutionV and a balanced array of strength 4 with index set {μ0,μ0,μ1,μ2,μ3,μ4} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fractionT and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2m factorial designT of resolution 2l+1 to be balanced is thatT is a balanced array of strength 2l with index set {μ0,μ1,μ2, ⋯,μ21} provided the information matrixM is nonsingular.

Design of a new balanced file organization scheme with the least redundancy

A new balanced file organization scheme of order two for binary-valued records is given which we call HUBFS 2 (Hiroshima University balanced file organization scheme). It can be constructed for a wide range of parameters as is in NBFS 2 . Moreover, it has the least redundancy among the file organization schemes of order two under a general class of probability distribution of records having the invariance property in permutation of attributes. Our scheme is superior to the corresponding NBFS 2 due to Chow as well as BFS 2 due to Abraham, Ghosh, and Ray-Chaudhuri so far as the redundancy is concerned.

Hyperclaw Decomposition of Complete Hypergraphs

Publisher Summary This chapter describes hyperclaw decomposition of complete hypergraphs. The chapter discusses a necessary condition and several sufficient conditions for the k-HC decomposability of a complete k-graph H m,k for k ≥3 are given. The 3-HC decomposability of H m,3 is given in some detail. With respect to the k -HC decomposability of a complete k-graph H m,k , the chapter describes some theorems.

Design of a balanced multiple-valued file-organization scheme with the least redundancy

A new balanced file-organization scheme of order two for multiple-valued records is presented. This scheme is called HUBMFS<subscrpt>2</subscrpt> (Hiroshima University Balanced Multiple-valued File-organization Scheme of order two). It is assumed that records are characterized by <italic>m</italic> attributes having <italic>n</italic> possible values each, and the query set consists of queries which specify values of two attributes. It is shown that the redundancy of the bucket (the probability of storing a record in the bucket) is minimized if and only if the structure of the bucket is a partite-claw. A necessary and sufficient condition for the existence of an HUBMFS<subscrpt>2</subscrpt>, which is composed exclusively of partite-claw buckets, is given. A construction algorithm is also given. The proposed HUBMFS<subscrpt>2</subscrpt> is superior to existing BMFS<subscrpt>2</subscrpt> (Balanced Multiple-valued File-organization Schemes of order two) in that it has the least redundancy among all possible BMFS<subscrpt>2</subscrpt>s having the same parameters and that it can be constructed for a less restrictive set of parameters.

Design of a balanced multiple-valued filing scheme of order two based on cyclically generated spread in finite projective geometry

The balanced multiple-valued filing scheme was defined by Ghosh and Abraham (1968) . They constructed there two types of balanced multiple-valued filing scheme of order two. One scheme was obtained by deleting a spread generated by parallel lines in a finite affine geometry EG ( t, s ) and the other was obtained by deleting a partial spread generated by all the lines in a finite projective geometry PG ( t, s ) which have one particular point in common. The idea of these methods of construction was generalized by Koch (1967) . In this paper, we shall give a new type of balanced multiple-valued filing scheme of order two constructed by deleting a cyclically generated spread in a finite t -dimensional projective geometry PG ( t, s ) where t + 1 is not prime. Since the spread identified with the set of attributes and the lines identified with the buckets can be generated cyclically in multiplicative representation of the points in PG(t, s) , the proposed scheme can be implemented easily.

Partition of a query set into minimal number of subsets having consecutive retrieval property

Abstract This paper is concerned with information retrieval. The basic problem is how to store large masses of data in such a way that whenever information regarding some particular aspect of the data is needed, such information is easily and efficiently retrieved. Work in this field is thus very important for organizations dealing with large classes of data. The consecutive retrieval (C-R) property defined by S.P. Ghosh is an important relation between a set of queries and a set of records. Its existence enables the design of information retrieval system with a minimal search time and no redundant storage in that the records can be organized in such a way that those pertinent to any query are stored in consecutive storage locations. The C-R property, however, can not exist between every arbitrary query set and every record set. A subset of the query set Q having the C-R property is called a C-R subset and a C-R subset having the maximum cardinality is called the maximal C-R subset. A partition of Q is called the C-R partition if every subset has the C-R property. A C-R partition with minimum number of subsets is called the minimal C-R partition. With respect to the set of all binary queries and the set of all binary records, it is shown that the maximal cardinality of a C-R subset is 2 l -1 where l is the number of attributes concerned. A combinatorial characterization of a maximal C-R subset is also given. A lower bound on the number of subsets in a C-R partition and several examples which attain the lower bound are given. A general procedure for obtaining a minimal C-R partition which attains the lower bound is given provided the number of attributes is even.

Design of a generalized balanced multiple-valued file organization scheme of order two

A file organization scheme in an information storage and retrieval system which will be called a generalized Hiroshima University balanced multiple-valued file organization scheme of order two (GHUBMFS2) is presented, where the information about the records is indexed by m attributes having n values. The number of buckets to be organized and the redundancy of the file are the same as those of an inverted file. The number of pointer fields to be attached to the accession number stored in a bucket is reduced to a minimum in this scheme. It can answer for all second order as well as first order queries by the access to one bucket and the traversal of its contents without any set operations.

Design of Optimal Balanced Filing Schemes

A gist of the design of optimal balanced filing schemes is discussed in connection with inverted schemes. The underlying idea is explained by introducing a multiple queries to adress transformation (MQAT) which yields a new less redundant storing scheme called HUBFS1. Essentials of our recent work on optimal balanced filing schemes are also introduced in relation to the construction of MQAT.