On the Comparison Complexity of the String Prefix-Matching Problem

In this paper we study the exact comparison complexity of the stringprefix-matching problem in the deterministic sequential comparison modelwith equality tests. We derive almost tight lower and upper bounds onthe number of symbol comparisons required in the worst case by on-lineprefix-matching algorithms for any fixed pattern and variable text. Unlikeprevious results on the comparison complexity of string-matching andprefix-matching algorithms, our bounds are almost tight for any particular pattern.We also consider the special case where the pattern and the text are thesame string. This problem, which we call the string self-prefix problem, issimilar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matchingalgorithm that is used in several comparison efficient string-matchingand prefix-matching algorithms, including in our new algorithm.We obtain roughly tight lower and upper bounds on the number of symbolcomparisons required in the worst case by on-line self-prefix algorithms.Our algorithms can be implemented in linear time and space in thestandard uniform-cost random-access-machine model

On Competitive On-Line Paging with Lookahead

This paper studies two methods for improving the competitive efficiency of on-line paging algorithms: in the first, the on-line algorithm canuse more pages; in the second, it is allowed to have a look-ahead, or inother words, some partial knowledge of the future. The paper considers anew measure for the look-ahead size as well as Young's resource-boundedlook-ahead and proves that both measures have the attractive propertythat the competitive efficiency of an on-line algorithm with k extra pagesand look-ahead l depends on k+l. Hence, under these measures, an on-linealgorithm has the same benefit from using an extra page or knowing anextra bit of the future

On the Comparison Complexity of the String Prefix-Matching Problem

In this paper we study the exact comparison complexity of the string prefix-matching problem in the deterministic sequential comparison model with equality tests. We derive almost tight lower and upper bounds on the number of symbol comparisons required in the worst case by on-line prefix-matching algorithms for any fixed pattern and variable text. Unlike previous results on the comparison complexity of string-matching and prefix-matching algorithms, our bounds are almost tight for any particular pattern. We also consider the special case where the pattern and the text are the same string. This problem, which we call the string self-prefix problem, is similar to the pattern preprocessing step of the Knuth-Morris-Pratt stringmatching algorithm that is used in several comparison efficient stringmatching and prefix-matching algorithms, including in our new algorithm. We obtain roughly tight lower and upper bounds on the number of symbol comparisons required in the worst case..