Abstract
On-demand string sorting is the problem of preprocessing a set of n strings to allow subsequent queries of finding the k < n lexicographically smallest strings (and afterwards the next k etc.) This on-demand variant strongly resembles the search engine queries which give you the best k-ranked pages recurringly.
We present a data structure that supports this in O(n) preprocessing time, and answers queries in O(logn) time. There is also a cost of O(N) time amortized over all operations, where N is the total length of the strings.
Our data structure is a heap of strings, which supports heapify and delete-mins. As it turns out, implementing a full heap with all operations is not that simple. For the sake of completeness we propose a heap with full operations based on balanced indexing trees that supports the heap operations in optimal times.
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Kent, C., Lewenstein, M., Sheinwald, D. (2007). On Demand String Sorting over Unbounded Alphabets. In: Ma, B., Zhang, K. (eds) Combinatorial Pattern Matching. CPM 2007. Lecture Notes in Computer Science, vol 4580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73437-6_5
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DOI: https://doi.org/10.1007/978-3-540-73437-6_5
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