max planck institut
informatik

# Philip Wellnitz

Max Planck Institute for Informatics
Department 1: Algorithms and Complexity
Campus E1 4, Room 324
66123, Saarbrücken
Germany

Email: wellnitzmpi-inf.mpg.de

I am a post-doctoral researcher at the Max Planck Institute for Informatics.

## Research Interests

• Obtaining (provably) best-possible algorithms by designing faster algorithms and matching (conditional) lower bounds
• (Approximate) String Matching and in general algorithms on strings
• Counting Problems, also in parameterized settings (especially problems related to graph homomorphisms)

I am happy to collaborate on any level. In particular, if you happen to be interested in doing an internship or thesis with me, feel free to contact me with informal inquiries; you may want to mention one of my papers (see below) that you read and liked (so that I get an idea about the kind of problems you would like to work on). Note that any internship applications will still have to go through the general internship program that can be found here; also note that there are no spots left for Summer 2023 anymore.

## Selected Publications

The following lists contain only selected publications. Consult dblp for a more complete list of publications.

## Approximate String Matching

 We give an \tilde{O}(n + n^0.5 k^1.5) algorithm for computing the weighted edit distance k between two strings. We prove that our algorithm is optimal for n^0.5 ≤ k ≤ n under the APSP hypothesis. We give an O(n + n/m k^3.5) algorithm for PM with edits. This is the first improvement of Cole and Hariharan's [CH'02] O(n + n/m k^4) algorithm for the problem.

## Counting (Small) Patterns in Graphs

 with Marc Roth and Johannes Schmitt We show that for any (non-trivial) monotone graph property Φ, counting all induced subgraphs of a graph that satisy Φ is #W[1]-hard and no significant improvement upon the brute-force algorithms is possible (unless ETH fails). with Marc Roth We show that any problem P in #W[1] (or W[1]) is equivalent to the problem of counting homomorphisms between graphs of graph classes H(P) and G(P).

## Code

• tikz-kneser: A tikz-library for drawing Kneser graphs.
• SOSML: An interpreter for SML running in your browser, check it out at sosml.org. Alternatively, write your SML code in the text box below and click “interpret”.
Written at Saarland University together with Julian Baldus, Julian Dörfler, Jesko Dujmovic, Marvin Hofmann and Dominik Luche

• Code of other projects is available on my GitHub profile