Hashing Methods for Temporal Data - Computer Science - Boston ...

KOLLIOS AND TSOTRAS: HASHING METHODS FOR TEMPORAL DATA 17
Fig. 7. a) Query, b) update, and c) space performance for PPLH-s on a uniform workload with varying values of the usefulness parameter u.
discussion in this paper assumes temporal membership
queries over a linear transaction-time evolution. It is
interesting to investigate hashing in branched transaction
environments [25].
APPENDIX
UPDATE AND SPACE ANALYSIS OF THE
EVOLVING-LIST APPROACH
The NT arrays facilitate the efficient location of the next list
page. However,if,during the usefulness period of page A,
its next page changes often,array NT…A† can become full.
Assume this scenario happens at time t and let C be the
page before page A. Page A is then artificially replaced in the
list by page A 0 . The B r part of A 0 is a copy of the B r part of
page A thus, A 0 is useful),but NT…A 0 † is empty. A new
entry is added in NT…C† with the pid of A 0 and the first
entry of NT…A 0 † stores the pid of the page if any) that was
after page A at t. If all list pages until page A had their
NT arrays full,the above process of artificially turning
useful pages to nonuseful ones can propagate all the way to
the beginning of the list. If the first list page is replaced,
array FT j is updated. However,this does not happen often.
Fig. 8 shows an example of how arrays NT…† and FT j are
maintained. From each page,only the NT array is shown.
In this example, B-B r ˆ 4 entries. At time t 6 ,array NT…A†
fills up and an artificial copy of page A is created with array
NT…A 0 †. Array NT…C† is also updated about the artificially
created new page.
The artificial creation of page A 0 provides faster query
processing. If instead of creating page A 0 , NT…A† is allowed
to grow over the B-B r area of page A using additional
pages),the last entry on NT…C† still points to page A.
Locating the next page after C at time t would lead to page A,
but then a serial search among the pages of array NT…A† is
needed. Clearly,this approach is inefficient if the page in
front of page A changes many times. Using the artificial
pages,the next useful list page for any time of interest is
found by one I/O! This technique is a generalization of the
backward updating technique used in [35].
In the evolving-list approach,copying occurs when a
page turns nonuseful or when a page is artificially replaced.
We first consider the evolving-list without the artificial page
replacements and show that the copying due to page
usefulness is linear to the total number of real oid changes.
We use an amortization argument that counts the number
of real changes that occur to a page before this page
becomes nonuseful. A useful page can become nonuseful