… More generally, a few algorithms will have running time O(f(k)nc), where c is a constant
and f(k) is an arbitrary function that does not depend on n but depends only on some other – …

… First we use the function f k ∈ F to compute a square matrix M k , such that \({{{{\bf{M}}}}}_{ij}^{k}={f}^{\,k}(A,i,j)\).
The dimension of M k is \(\frac{S}{B}\times \frac{S}{B}\), where B …

… ones in \(F\) (respectively, in \(L\)), using \(O(k)\) words of space. Let \(F'[1..\alpha ]\) be the
array such that \(F'[i]\) equals the number of intervals \([p..q]\) such that \(p\) is the \(i\)th one in \(…

… We call f-cover a set of substrings of s with the following property: for every substring v not
in … We can compute an f-cover of s in overall O(|Σ|λ log |s|) + |s| log |Σ| + o(|s| log |Σ|) bits of …

… We use f (c) to denote the frequency of character c in S, f (c,b… of a minimal perfect hash function
F that maps every element in S … We also use a table lcp[1..n] that stores at index F (xi ) the …

… the current value of f, where y is the inverse of v.count, and we start from such value of f when
visiting the subgraph of G that starts at v. To support weighted ancestor queries on f and T (…

Presenting the fundamental algorithms and data structures that power bioinformatics
workflows, this book covers a range of topics from the foundations of sequence analysis (…

… (F)\) the sequence of characters produced by a nonterminal F … F corresponds to an interval
in \(\pi (F)\). Given a nonterminal … F we denote the set of all marked nodes in the parse tree of F…

Given a string T on an alphabet of size sigma, we describe a bidirectional Burrows-Wheeler
index that takes O (| T| log sigma) bits of space, and that supports the addition and removal …

The unidirectional and bidirectional matching statistics between two strings s and t on alphabet
Σ, and the shortest unique substrings of a single string t, are the cornerstone of a number …