Raphaël Clifford

Classical boson sampling algorithms with superior performance to near-term experiments

Alex Neville, Chris Sparrow, Raphaël Clifford, Eric Johnston, Patrick M. Birchall, Ashley Montanaro, and Anthony Laing1∗ Quantum Engineering and Technology Laboratories, School of Physics and Department of Electrical and Electronic Engineering, University of Bristol, UK Department of Physics, Imperial College London, UK Department of Computer Science, University of Bristol, UK School of Mathematics, University of Bristol, UK

A Black Box for Online Approximate Pattern Matching

We present a deterministic black box solution for online approximate matching. Given a pattern of length mand a streaming text of length nthat arrives one character at a time, the task is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives. Our solution requires

Scheduling algorithms for procrastinators

O(\Sigma_{j=1}^{\log_2{m}} T(n,2^{j-1})/n)

Generalised Matching

time for each input character, where T(n,m) is the total running time of the best offline algorithm. The types of approximation that are supported include exact matching with wildcards, matching under the Hamming norm, approximating the Hamming norm, k-mismatch and numerical measures such as the L 2 and L 1 norms. For these examples, the resulting online algorithms take O(log2m),

Element Distinctness, Frequency Moments, and Sliding Windows

O(\sqrt{m\log{m}})

Dictionary Matching in a Stream

, O(log2m/i¾?2),

Restricted common superstring and restricted common supersequence

O(\sqrt{k \log k} \log{m})

Pseudo-realtime pattern matching: closing the gap

, O(log2m) and

Lower bounds for online integer multiplication and convolution in the cell-probe model

O(\sqrt{m\log{m}})

Pattern matching under polynomial transformation

time per character respectively. The space overhead is O(m) which we show is optimal.