perm filename DEC.XGP[BIB,CSR] blob sn#386192 filedate 1978-10-10 generic text, type T, neo UTF8
/LMAR=0/XLINE=10/FONT#0=METS/FONT#1=BAXM30/FONT#2=METSB/FONT#3=FIX25/FONT#4=MATH30/FONT#5=SUP/FONT#6=MS25/FONT#8=SUB/FONT#9=GACL25
␈↓ α∧␈↓December Reports␈↓ u1

␈↓"β␈↓ α∧␈↓␈↓ ∧g␈↓αMOST RECENT CS REPORTS ␈↓↓-␈↓α DECEMBER 1978␈↓

␈↓"β␈↓ α∧␈↓    Listed␈α∞below␈α∞are␈α∞abstracts␈α∞of␈α∞the␈α∞most␈α∞recent␈α∞reports␈α∞published␈α∞by␈α∞the␈α∞Computer␈α∞Science␈α∂Department␈α∞of
␈↓ α∧␈↓Stanford University.

␈↓"β␈↓ α∧␈↓    TO␈α
REQUEST␈α
REPORTS:  Check␈α
the␈α
appropriate␈α
places␈α
on␈α
the␈α
enclosed␈α
order␈α
form,␈α
and␈α
return␈α
the␈α
entire␈α	order
␈↓ α∧␈↓form␈αλpage␈αλ(including␈αλmailing␈αλlabel)␈αλby␈αλDecember␈αλ4,␈αλ1978.␈αλ In␈αλmany␈αλcases␈αλwe␈αλcan␈αλprint␈αλonly␈αλa␈αλlimited␈α	number␈αλof
␈↓ α∧␈↓copies,␈αand␈αrequests␈α
will␈αbe␈αfilled␈α
on␈αa␈αfirst␈α
come,␈αfirst␈αserve␈αbasis.␈α
 In␈αthe␈αcode␈α
(FREE)␈αis␈αprinted␈α
on␈αyour
␈↓ α∧␈↓mailing␈α
label,␈α
you␈α
will␈αnot␈α
be␈α
charged␈α
for␈αhardcopy.␈α
 This␈α
exemption␈α
from␈αpayment␈α
is␈α
limited␈α
primarily␈αto
␈↓ α∧␈↓libraries.␈α (The␈αcosts␈αshown␈αinclude␈αall␈αapplicable␈αsales␈αtaxes.␈α PLEASE␈αSEND␈αNO␈αMONEY␈αNOW,␈αWAIT␈α
UNTIL
␈↓ α∧␈↓YOU GET AN INVOICE.)

␈↓"β␈↓ α∧␈↓    ALTERNATIVELY:␈α Copies␈αof␈α
most␈αStanford␈αCS␈αReports␈α
may␈αbe␈αobtained␈αby␈α
writing␈α(about␈α2␈α
months␈αafter
␈↓ α∧␈↓MOST␈αRECENT␈αCS␈αREPORTS␈αlisting)␈αto␈αNATIONAL␈αTECHNICAL␈αINFORMATION␈αSERVICE,␈α5285␈αPort␈αRoyal␈αRoad,
␈↓ α∧␈↓Springfield,␈αVirginia␈α22161.␈α Stanford␈αPh.D.␈αtheses␈αare␈αavailable␈αfrom␈αUNIVERSITY␈αMICROFILMS,␈α300␈αNorth
␈↓ α∧␈↓Zeeb Road, Ann Arbor, Michigan 48106.
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α681  SET REPRESENTATION AND SET INTERSECTION
␈↓"β␈↓ α∧␈↓αAuthor:␈↓  Luis Trabb Pardo␈↓ &(Thesis)

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    This␈α	work␈αλdiscusses␈α	the␈α	representation␈αλand␈α	manipulation␈αλof␈α	sets␈α	based␈αλon␈α	two␈α	different␈αλconcepts:
␈↓ α∧␈↓tries, and hashing functions.

␈↓"β␈↓ α∧␈↓    The␈α∞sets␈α∞considered␈α∞here␈α∞are␈α∞assumed␈α∞to␈α∞be␈α
static:␈α∞ once␈α∞created,␈α∞there␈α∞will␈α∞be␈α∞no␈α∞further␈α∞insertions␈α
or
␈↓ α∧␈↓deletions.␈α For␈α
both␈αtrie␈↓↓-␈↓␈αand␈α
hash␈↓↓-␈↓based␈αstrategies,␈αa␈α
series␈αof␈αrepresentation␈α
is␈αintroduced␈α
which␈αtogether
␈↓ α∧␈↓with␈αλthe␈α	availability␈αλof␈α	preprocessing␈αλreduces␈α	the␈αλaverage␈α	sizes␈αλof␈α	the␈αλsets␈α	to␈αλnearly␈α	optimal␈αλvalues,␈α	yet␈αλretains
␈↓ α∧␈↓the inherently good retrieval characteristics.

␈↓"β␈↓ α∧␈↓    The␈αintersection␈αprocedure␈αfor␈α
trie␈↓↓-␈↓based␈αrepresentations␈αis␈αbased␈αon␈α
the␈αtraversal␈αin␈αparallel␈αof␈α
the␈αtries
␈↓ α∧␈↓representing␈αthe␈α
sets␈αto␈α
be␈αintersected,␈αand␈α
it␈αbehaves␈α
like␈αa␈α
series␈αof␈αbinary␈α
searches␈αwhen␈α
the␈αsets␈α
to␈αbe
␈↓ α∧␈↓intersected␈α	are␈α
of␈α	very␈α
different␈α	sizes.␈α
 Hashed␈α	intersection␈α	runs␈α
very␈α	fast.␈α
 The␈α	average␈α
time␈α	is␈α
proportional␈α	to
␈↓ α∧␈↓the␈αλsize␈α	of␈αλthe␈α	smallest␈αλset␈αλto␈α	be␈αλintersected␈α	and␈αλis␈αλindependent␈α	of␈αλthe␈α	number␈αλof␈αλsets␈α	(except␈αλfor␈α	the␈αλintersection
␈↓ α∧␈↓set itself which has to be checked for every set).
␈↓"β␈↓ α∧␈↓No. of pages:  85
␈↓"β␈↓ α∧␈↓Cost:  $ 4.10
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α682  PARSING FLOWCHARTS AND SERIES␈↓↓-␈↓αPARALLEL GRAPHS
␈↓"β␈↓ α∧␈↓αAuthor:␈↓  Jacobo Valdes ␈↓ &(Thesis)

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    The␈αmain␈αresults␈α
presented␈αin␈αthis␈αwork␈α
are␈αan␈αalgorithm␈αfor␈α
the␈αrecognition␈αof␈αGeneral␈α
Series
␈↓ α∧␈↓Parallel (GSP) digraphs and an approach to the structural analysis of the control flow graphs of programs.

␈↓"β␈↓ α∧␈↓    The␈α
GSP␈α	recognition␈α
algorithm␈α
determines␈α	in␈α
␈↓↓O(n+m)␈↓␈α	steps␈α
whether␈α
an␈α	acyclic␈α
digraph␈α	with␈α
␈↓↓n␈↓␈α
vertices␈α	and
␈↓ α∧␈↓␈↓↓m␈↓␈α	edges␈αλis␈α	GSP,␈α	and␈αλif␈α	it␈αλis,␈α	describes␈α	its␈αλstructure␈α	in␈αλterms␈α	of␈α	two␈αλsimple␈α	operations␈αλon␈α	digraphs.␈α	 The␈αλalgorithm
␈↓ α∧␈↓is based on the relationship between GSP digraphs and the more standard class of TTSP multidigraphs.

␈↓"β␈↓ α∧␈↓    Our␈α∪approach␈α∀to␈α∪the␈α∪analysis␈α∀of␈α∪flow␈α∪graphs␈α∀uses␈α∪the␈α∪triconnected␈α∀components␈α∪algorithm␈α∀to␈α∪find
␈↓ α∧␈↓December Reports␈↓ u2

␈↓"β␈↓ α∧␈↓single␈↓↓-␈↓entry,␈α
single␈↓↓-␈↓exit␈α
regions.␈α Under␈α
certain␈α
conditions␈α␈↓↓-␈↓␈↓↓-␈↓␈α
that␈α
we␈α
identify␈α␈↓↓-␈↓␈↓↓-␈↓␈α
this␈α
method␈αwill␈α
produce
␈↓ α∧␈↓structural␈α
information␈αsuitable␈α
for␈α
the␈αglobal␈α
flow␈αanalysis␈α
of␈α
control␈αflow␈α
graphs␈α
in␈αtime␈α
proportional␈αto␈α
the
␈↓ α∧␈↓numer of vertices and edges of the graph being analyzed.
␈↓"β␈↓ α∧␈↓No. of pages:  233
␈↓"β␈↓ α∧␈↓Available in microfiche only.
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α683  STORING A SPARSE TABLE
␈↓"β␈↓ α∧␈↓αAuthor:␈↓  Robert Endre Tarjan

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    The␈αλproblem␈αλof␈α	storing␈αλand␈αλsearching␈α	large␈αλsparse␈αλtables␈α	arises␈αλin␈αλcompiling␈α	and␈αλin␈αλother␈α	areas␈αλof
␈↓ α∧␈↓computer␈α	science.␈α	 The␈α	standard␈α	technique␈α	for␈α	storing␈α
such␈α	tables␈α	is␈α	hashing,␈α	but␈α	hashing␈α	has␈α
poor␈α	worst␈↓↓-␈↓case
␈↓ α∧␈↓performance.␈αλ We␈α	consider␈αλgood␈α	worst␈↓↓-␈↓case␈αλmethods␈αλfor␈α	storing␈αλa␈α	table␈αλof␈αλ␈↓↓n␈↓␈α	entries,␈αλeach␈α	an␈αλinteger␈α	between␈αλ␈↓↓O␈↓
␈↓ α∧␈↓and␈α	␈↓↓N-1␈↓.␈α	 For␈α	dynamic␈α	tables,␈α	in␈α	which␈α	look␈↓↓-␈↓ups␈α	and␈α	table␈α	additions␈α	are␈α	intermixed,␈α	the␈α	use␈α	of␈α	a␈α	trie␈α	requires
␈↓ α∧␈↓␈↓↓O(kn)␈↓␈α	storage␈α	and␈α	allows␈α	␈↓↓O(log␈↓#vk␈↓#(N/n))␈↓␈α	worst␈↓↓-␈↓case␈α	access␈α	time,␈α	where␈α	␈↓↓k␈↓␈α	is␈α	an␈α	arbitrary␈α	parameter.␈α	 For␈αλstatic
␈↓ α∧␈↓tables,␈αin␈αwhich␈αthe␈αentire␈αtable␈αis␈αconstructed␈αbefore␈αany␈αlook␈↓↓-␈↓ups␈αare␈αmade,␈αwe␈αpropose␈αa␈αmethod␈αwhich
␈↓ α∧␈↓requires␈α	␈↓↓O(n␈α	log␈↓#
(l)␈↓#n)␈↓␈α	storage␈α	and␈α	allow␈α	␈↓↓O(l␈α	log␈↓#vn␈↓#␈α	N)␈↓␈α	access␈α	time,␈α	where␈α	␈↓↓l␈↓␈α	is␈α	an␈α	arbitrary␈α
parameter.␈α	 Choosing
␈↓ α∧␈↓␈↓↓l = log␈↓#
*␈↓# n␈↓ gives a method with ␈↓↓O(n)␈↓ storage and ␈↓↓O((log␈↓#
*␈↓# n)(log␈↓#vn␈↓# N))␈↓ access time.
␈↓"β␈↓ α∧␈↓No. of pages:  23
␈↓"β␈↓ α∧␈↓Cost:  $ 2.35
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α684  THE MATRIX INVERSE EIGENVALUE PROBLEM FOR PERIODIC JACOBI MATRICES
␈↓"β␈↓ α∧␈↓αAuthors:␈↓  D. L. Boley and G. H. Golub␈↓ 
USU326 P30␈↓↓-␈↓64

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    A␈αλstable␈αλnumerical␈αλalgorithm␈αλis␈αλpresented␈αλfor␈α	generating␈αλa␈αλperiodic␈αλJacobi␈αλmatrix␈αλfrom␈αλtwo␈α	sets␈αλof
␈↓ α∧␈↓eigenvalues␈α∞and␈α∞the␈α∞product␈α∞of␈α∞the␈α∞off␈↓↓-␈↓diagonal␈α
elements␈α∞of␈α∞the␈α∞matrix.␈α∞ The␈α∞algorithm␈α∞requires␈α∞a␈α
simple
␈↓ α∧␈↓generalization␈αof␈αthe␈αLanczos␈αalgorithms.␈α It␈αis␈αshown␈αthat␈αthe␈αmatrix␈αis␈αnot␈αunique,␈αbut␈αthe␈αalgorithm␈αwill
␈↓ α∧␈↓generate all possible solutions.
␈↓"β␈↓ α∧␈↓No. of pages:  18
␈↓"β␈↓ α∧␈↓Available in microfiche only.
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α685  SPARSE AND PARALLEL MATRIX COMPUTATIONS
␈↓"β␈↓ α∧␈↓αAuthor:␈↓  Franklin Tai␈↓↓-␈↓cheung Luk␈↓ &(Thesis)

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    This␈α
thesis␈α
deals␈α	with␈α
four␈α
important␈α
matrix␈α	problems:␈α
 (1)␈α
the␈α	application␈α
of␈α
many␈α
variants␈α	of
␈↓ α∧␈↓the␈α∂conjugate␈α∂gradient␈α∞method␈α∂for␈α∂solving␈α∂matrix␈α∞equations,␈α∂(2)␈α∂the␈α∂solution␈α∞of␈α∂lower␈α∂and␈α∂upper␈α∞bounds
␈↓ α∧␈↓quadratic␈α	programs␈α	associated␈α
with␈α	M␈↓↓-␈↓matrices,␈α	(3)␈α
the␈α	construction␈α	of␈α	a␈α
Block␈α	Lanczos␈α	method␈α
for␈α	computing
␈↓ α∧␈↓the␈αgreatest␈α
singular␈αvalues␈α
of␈αa␈αmatrix,␈α
and␈α(4)␈α
the␈αcomputation␈αof␈α
the␈αsingular␈α
value␈αdecomposition␈α
of␈αa
␈↓ α∧␈↓matrix of the ILLIAC␈↓↓-␈↓IV computer.
␈↓"β␈↓ α∧␈↓No. of pages:  168
␈↓"β␈↓ α∧␈↓Available in microfiche only.
␈↓"β␈↓ α∧␈↓␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓-␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓↓␈↓β␈↓
␈↓"β␈↓ α∧␈↓␈↓αSTAN␈↓↓-␈↓αCS␈↓↓-␈↓α78␈↓↓-␈↓α686  EXTERNAL HASHING SCHEMES FOR COLLECTIONS OF DATA STRUCTURES
␈↓"β␈↓ α∧␈↓αAuthor(s):␈↓  Richard J. Lipton, Arnold L. Rosenberg and Andrew C. Yao

␈↓"β␈↓ α∧␈↓    ␈↓αAbstract:␈↓    We␈α
study␈α	the␈α
use␈α
of␈α	external␈α
hashing␈α	schemes␈α
for␈α
storing␈α	broad␈α
classes␈α	of␈α
data␈α
structures.␈α	 Our
␈↓ α∧␈↓general␈α∂framework␈α∂considers␈α∞a␈α∂class␈α∂of␈α∂data␈α∞structures␈α∂partitioned␈α∂into␈α∂smaller␈α∞classes␈α∂by␈α∂the␈α∂number␈α∞of
␈↓ α∧␈↓positions␈αλin␈α	the␈αλstructure.␈α	 For␈αλinstance,␈α	we␈αλcould␈α	start␈αλwith␈α	the␈αλclass␈α	of␈αλall␈α	binary␈αλtrees␈α	and␈αλpartition␈α	that␈αλclass
␈↓ α∧␈↓December Reports␈↓ u3

␈↓"β␈↓ α∧␈↓into␈α∂the␈α∂subclasses␈α⊂␈↓↓C␈↓␈↓#v1␈↓#,␈↓↓C␈↓␈↓#v2␈↓#,...␈α∂,␈α∂each␈α∂␈↓↓C␈↓#vn␈↓#␈↓␈α⊂comprising␈α∂all␈α∂␈↓↓n␈↓␈↓↓-␈↓node␈α∂binary␈α⊂trees.␈α∂ The␈α∂main␈α⊂results␈α∂establish
␈↓ α∧␈↓nonconstructively␈α∞the␈α∞existence␈α∞of␈α∞an␈α∞external␈α∞hashing␈α∞scheme␈α∞␈↓↓h␈↓#vn␈↓#␈↓␈α∞with␈α∞␈↓↓O(n)␈↓␈α∞␈↓↓-␈↓storage␈α∞demand␈α∞and␈α
␈↓↓O(1)␈↓
␈↓ α∧␈↓␈↓↓-␈↓expected␈αaccess␈αtime,␈αthat␈αwill␈αstore␈αany␈αstructure␈αin␈α␈↓↓C␈↓␈↓#v1␈↓#␈↓↓∪C␈↓␈↓#v2␈↓#␈↓↓∪...∪C␈↓#vn␈↓#␈↓␈α,␈αprovided␈α␈↓↓C␈↓#vn␈↓#␈↓␈αcontains␈αa␈αnumber␈αof
␈↓ α∧␈↓structures␈αgrowing␈αat␈αmost␈αexponentially␈αin␈α␈↓↓n␈↓.␈α Classes␈αof␈αdata␈αstructures␈αsubsumed␈αby␈αthese␈αresults␈αinclude
␈↓ α∧␈↓ragged arrays, binary trees, string␈↓↓-␈↓indexed arrays, and refinable arrays.
␈↓"β␈↓ α∧␈↓No. of pages:  33
␈↓"β␈↓ α∧␈↓Cost:  $ 2.65
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␈↓"β␈↓ α∧␈↓αAuthor:␈↓

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␈↓"β␈↓ α∧␈↓αAuthor:␈↓

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