Tight upper and lower bounds on suffix tree breadth
نویسندگان
چکیده
The suffix tree — the compacted trie of all suffixes a string is most important and widely-used data structure in processing. We consider natural combinatorial question about trees: for S length n, how many nodes νS(d) can there be at (string) depth d its tree? prove ν(n,d)=maxS∈ΣnνS(d) O((n/d)log(n/d)), show that this bound asymptotically tight, describing strings which Ω((n/d)log(n/d)).
منابع مشابه
On Suffix Tree Breadth
The suffix tree — the compacted trie of all the suffixes of a string — is the most important and widely-used data structure in string processing. We consider a natural combinatorial question about suffix trees: for a string S of length n, how many nodes νS(d) can there be at (string) depth d in its suffix tree? We prove ν(n, d) = maxS∈Σn νS(d) is O((n/d) logn), and show that this bound is almos...
متن کاملUpper and lower bounds of symmetric division deg index
Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In th...
متن کاملUpper and lower bounds for numerical radii of block shifts
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...
متن کاملAlmost Tight Upper Bounds for Lower Envelopes in Higher Dimensions
We show that the combinatorial complexity of the lower envelope of n surfaces or surface patches in dspace ( d 2 3), all algebraic of constant maximum degree, and bounded by algebraic surfaces of constant maximum degree, is O(rkl+') , for any E > 0; the constant of proportionality depends on E , d, and the shape and degree of the surface patches and of their boundaries. This is the first nontri...
متن کاملUpper and Lower Bounds for Tree-Like Cutting Planes Proofs
In this paper we study the complexity of Cutting Planes (CP) refutations, and tree-like CP refutations. Tree-like CP proofs are natural and still quite powerful. In particular, the propositional pigeonhole principle (PHP) has been shown to have polynomial-sized tree-like CP proofs. Our main result shows that a family of tautologies, introduced in this paper requires exponential-sized tree-like ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2021
ISSN: ['1879-2294', '0304-3975']
DOI: https://doi.org/10.1016/j.tcs.2020.11.037