Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Cost of Unsuccessful Searches in Search Trees with Two-way
  Comparisons   Search trees are commonly used to implement access operations to a set of
stored keys. If this set is static and the probabilities of membership queries
are known in advance, then one can precompute an optimal search tree, namely
one that minimizes the expected access cost. For a non-key query, a search tree
can determine its approximate location by returning the inter-key interval
containing the query. This is in contrast to other dictionary data structures,
like hash tables, that only report a failed search. We address the question
"what is the additional cost of determining approximate locations for non-key
queries"? We prove that for two-way comparison trees this additional cost is at
most 1. Our proof is based on a novel probabilistic argument that involves
converting a search tree that does not identify non-key queries into a random
tree that does.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci