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C00005 00004	%3STAN-CS-78-681  SET REPRESENTATION AND SET INTERSECTION
C00009 00005	%3STAN-CS-78-683  STORING A SPARSE TABLE
C00012 00006	%3STAN-CS-78-685  SPARSE AND PARALLEL MATRIX COMPUTATIONS
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%3MOST RECENT CS REPORTS - DECEMBER 1978%1

@Listed below are abstracts of the most recent reports published by the Computer
Science Department of Stanford University.

@TO REQUEST REPORTS:##Check the appropriate places on the enclosed order form,
and return the entire order form page (including mailing label) by
December 4, 1978.
In many cases we can print only a limited number of copies, and requests will
be filled on a first come, first serve basis.  In the code (FREE) is printed
on your mailing label, you will not be charged for hardcopy.  This exemption
from payment is limited primarily to libraries.  (The costs shown include all
applicable sales taxes.  PLEASE SEND NO MONEY NOW, WAIT UNTIL YOU GET AN INVOICE.)

@ALTERNATIVELY:  Copies of most Stanford CS Reports may be obtained by writing
(about 2 months after MOST RECENT CS REPORTS listing) to NATIONAL TECHNICAL
INFORMATION SERVICE, 5285 Port Royal Road, Springfield, Virginia 22161.  Stanford
Ph.D. theses are available from UNIVERSITY MICROFILMS, 300 North Zeeb Road,
Ann Arbor, Michigan 48106.
.begin nofill
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-681  SET REPRESENTATION AND SET INTERSECTION
%3Author:%1  Luis Trabb Pardo↔(Thesis)
.end
@%3Abstract:%1@This work discusses the representation and manipulation of sets
based on two different concepts:  tries, and hashing functions.

@The sets considered here are assumed to be static:  once created, there will
be no further insertions or deletions.  For both trie- and hash-based strategies,
a series of representation is introduced which together with the availability
of preprocessing reduces the average sizes of the sets to nearly optimal values,
yet retains the inherently good retrieval characteristics.

@The intersection procedure for trie-based representations is based on the
traversal in parallel of the tries representing the sets to be intersected, and
it behaves like a series of binary searches when the sets to be intersected are
of very different sizes.  Hashed intersection runs very fast.  The average time
is proportional to the size of the smallest set to be intersected and is
independent of the number of sets (except for the intersection set itself which
has to be checked for every set).
.break
.begin nofill
No. of pages:  85
Cost:  $ 4.10
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-682  PARSING FLOWCHARTS AND SERIES-PARALLEL GRAPHS
%3Author:%1  Jacobo Valdes ↔(Thesis)
.end
@%3Abstract:%1@The main results presented in this work are an algorithm for the
recognition of General Series Parallel (GSP) digraphs and an approach to the
structural analysis of the control flow graphs of programs.

@The GSP recognition algorithm determines in %2O(n+m)%1 steps whether an acyclic
digraph with %2n%1 vertices and %2m%1 edges is GSP, and if it is, describes its
structure in terms of two simple operations on digraphs.  The algorithm is based
on the relationship between GSP digraphs and the more standard class of TTSP
multidigraphs.

@Our approach to the analysis of flow graphs uses the triconnected components
algorithm to find single-entry, single-exit regions.  Under certain
conditions -- that we identify -- this method will produce structural information
suitable for the global flow analysis of control flow graphs in time proportional
to the numer of vertices and edges of the graph being analyzed.
.break
.begin nofill
No. of pages:  233
Available in microfiche only.
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-683  STORING A SPARSE TABLE
%3Author:%1  Robert Endre Tarjan
.end
@%3Abstract:%1@The problem of storing and searching large sparse tables arises
in compiling and in other areas of computer science.  The standard technique
for storing such tables is hashing, but hashing has poor worst-case performance.
We consider good worst-case methods for storing a table of %2n%1 entries, each
an integer between %2O%1 and %2N-1%1.  For dynamic tables, in which look-ups 
and table
additions are intermixed, the use of a trie requires %2O(kn)%1 storage and
allows %2O(log↓k(N/n))%1 worst-case access time, where %2k%1 is an arbitrary
parameter.  For static tables, in which the entire table is constructed before
any look-ups are made, we propose a method which requires %2O(n log∩[(l)]n)%1
storage and allow %2O(l log↓n N)%1 access time, where %2l%1 is an arbitrary
parameter.  Choosing %2l = log↑* n%1 gives a method with %2O(n)%1 storage and
%2O((log↑* n)(log↓n N))%1 access time.
.begin nofill
No. of pages:  23
Cost:  $ 2.35
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-684  THE MATRIX INVERSE EIGENVALUE PROBLEM FOR PERIODIC JACOBI MATRICES
%3Authors:%1  D. L. Boley and G. H. Golub↔SU326 P30-64
.end
@%3Abstract:%1@A stable numerical algorithm is presented for generating a
periodic Jacobi matrix from two sets of eigenvalues and the product of the
off-diagonal elements of the matrix.  The algorithm requires a simple generalization
of the Lanczos algorithms.  It is shown that the matrix is not unique, but the
algorithm will generate all possible solutions.
.begin nofill
No. of pages:  18
Available in microfiche only.
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-685  SPARSE AND PARALLEL MATRIX COMPUTATIONS
%3Author:%1  Franklin Tai-cheung Luk↔(Thesis)
.end
@%3Abstract:%1@This thesis deals with four important matrix problems:  (1) the
application of many variants of the conjugate gradient method for solving matrix
equations, (2) the solution of lower and upper bounds quadratic programs
associated with M-matrices, (3) the construction of a Block Lanczos method for
computing the greatest singular values of a matrix, and (4) the computation of
the singular value decomposition of a matrix of the ILLIAC-IV computer.
.begin nofill
No. of pages:  168
Available in microfiche only.
%4-------------------------------------------------------------------------------------%1
%3STAN-CS-78-686  EXTERNAL HASHING SCHEMES FOR COLLECTIONS OF DATA STRUCTURES
%3Author(s):%1  Richard J. Lipton, Arnold L. Rosenberg and Andrew C. Yao
.end
@%3Abstract:%1@We study the use of external hashing schemes for storing broad
classes of data structures.  Our general framework considers a class of data
structures partitioned into smaller classes by the number of positions in the
structure.  For instance, we could start with the class of all binary trees
and partition that class into the subclasses %2C%1↓1,%2C%1↓2,...%1 , each %2C↓n%1
comprising all %2n%1-node binary trees.  The main results establish
nonconstructively the existence of an external hashing scheme %2h↓n%1 with
%2O(n)%1 -storage demand and %2O(1)%1 -expected access time, that will store
any structure in %2C%1↓1%2α∪C%1↓2%2α∪...α∪C↓n%1 , provided %2C↓n%1 contains a number
of structures growing at most exponentially in %2n%1.  Classes of data
structures subsumed by these results include ragged arrays, binary trees,
string-indexed arrays, and refinable arrays.
.begin nofill
No. of pages:  33
Cost:  $ 2.65
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%3Author:%1  
.end
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%3Author:%1  
.end
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