Benjamin Sach

Generalised Matching

Given a pattern p over an alphabet Σ p and a text t over an alphabet Σ t , we consider the problem of determining a mapping f from Σ p to

Time-Space trade-offs for longest common extensions

{\Sigma}_{t}^{+}

Parameterized Matching in the Streaming Model.

such that t = f (p 1 )f (p 2 )...f (p m ). This class of problems, which was first introduced by Amir and Nor in 2004, is defined by different constraints on the mapping f . We give NP-Completeness results for a wide range of conditions. These include when f is either many-to-one or one-to-one, when Σ t is binary and when the range of f is limited to strings of constant length. We then introduce a related problem we term pattern matching with string classes which we show to be solvable efficiently. Finally, we discuss an optimisation variant of generalised matching and give a polynomial-time min

Dictionary Matching in a Stream

(1,\sqrt{k/OPT})

Sparse suffix tree construction in small space

-approximation algorithm for fixed k .

Pseudo-realtime pattern matching: closing the gap

We revisit the longest common extension (LCE) problem, that is, preprocess a string T into a compact data structure that supports fast LCE queries. An LCE query takes a pair (i,j) of indices in T and returns the length of the longest common prefix of the suffixes of T starting at positions i and j. We study the time-space trade-offs for the problem, that is, the space used for the data structure vs. the worst-case time for answering an LCE query. Let n be the length of T. Given a parameter τ, 1≤τ≤n, we show how to achieve either

Time-space trade-offs for longest common extensions

O({n}/{\sqrt{\tau}})

Pattern matching under polynomial transformation

space and O(τ) query time, or O(n/τ) space and

Pattern matching in multiple streams

O(\tau \log({|\ensuremath{\mathrm{LCE}} (i,j)|}/{\tau}))

Online Approximate Matching with Non-local Distances

query time, where