Extreme Value Statistics and Traveling Fronts: An Application to Computer Science
نویسندگان
چکیده
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer problem on a Cayley tree. We employ the techniques of traveling fronts to solve the polymer problem and translate back to derive exact asymptotic properties in the original search tree problem. The second mapping allows us not only to re-derive the already known results for random binary trees but to obtain new exact results for search trees where the entries arrive according to an arbitrary distribution, not necessarily randomly. Besides it allows us to derive the asymptotic shape of the full probability distribution of height and not just its moments. Our results are then generalized to m-ary search trees with arbitrary distribution.
منابع مشابه
Extreme value statistics and traveling fronts: application to computer science.
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem that is then further mapped to a modified directed polymer problem on a Cayley tree. We employ the techniques of traveling fronts to solve the polymer problem and translate back to derive exact asymptotic properties in th...
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ورودعنوان ژورنال:
- CoRR
دوره cond-mat/0109313 شماره
صفحات -
تاریخ انتشار 2001