# Søren Vind

I am a PhD student in the Algorithms, Logic and Graphs Section in the Department of Applied Mathematics and Computer Science at the Technical University of Denmark, from where I also received my BSc and MSc.

I am associated with the Managed Video as a Service Advanced Technology Foundation project.
The goal is to research and develop compressed data structures for indexing massive amounts of meta data that supports efficient queries.

My supervisors are Philip Bille and Inge Li Gørtz.
I work closely together with fellow PhD students Patrick Hagge Cording, Frederik Rye Skjoldjensen and Hjalte Wedel Vildhøj.

### Contact

DTU Compute
Building 322, Office 008
DK-2800 Kongens Lyngby
Denmark

Email: sovi@dtu.dk

## Research

My research interests are within fundamental algorithms and data structure problems, stringology, compression, computational geometry and distributed computing.

### Publications

• SWAT 2014: Colored Range Searching in Linear Space with Roberto Grossi.
Abstract
In colored range searching, we are given a set of $n$ colored points in $d \geq 2$ dimensions to store, and want to support orthogonal range queries taking colors into account. In the colored range counting problem, a query must report the number of distinct colors found in the query range, while an answer to the colored range reporting problem must report the distinct colors in the query range.

We give the first linear space data structure for both problems in two dimensions ($d=2$) with $o(n)$ worst case query time. We also give the first data structure obtaining almost-linear space usage and $o(n)$ worst case query time for points in $d > 2$ dimensions. Finally, we present the first dynamic solution to both counting and reporting with $o(n)$ query time for $d \geq 2$ and $d \geq 3$ dimensions, respectively.
• Theory of Computing Systems: String Indexing for Patterns with Wildcards with Philip Bille, Inge Li Gørtz, and Hjalte Wedel Vildhøj.
Arxiv version, Abstract, Conference version:
We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results.
• A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case.
• An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time.
• A time-space trade-off, generalizing the index by Cole et al. [STOC 2004].
Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest.
• WADS 2013: Fingerprints in Compressed Strings with Philip Bille, Patrick Hagge Cording, Inge Li Gørtz, Benjamin Sach, and Hjalte Wedel Vildhøj.
Full version (draft), Abstract
The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string $S$ of size $N$ compressed by a context-free grammar of size $n$ that answers fingerprint queries. That is, given indices $i$ and $j$, the answer to a query is the fingerprint of the substring $S[i,j]$. We present the first $O(n)$ space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get $O(\log N)$ query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get $O(\log \log N)$ query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time $O(\log N\log \ell)$ and $O(\log \ell \log\log \ell + \log\log N)$ for SLPs and Linear SLPs, respectively. Here, $\ell$ denotes the length of the LCE.
• Master's Thesis: String Indexing for Patterns with Wildcards with Hjalte Wedel Vildhøj.
Supervised by Philip Bille and Inge Li Gørtz.
Technical University of Denmark, August 8, 2011.

### Experiments

Motion Detection Indexing
There is source code available on Github for testing the performance of an index for motion detection data from surveillance video cameras.

## Conferences

• ICALP 2014
IT University of Copenhagen, Denmark
July 7-11 2014
• SWAT 2014
Presented Colored Range Searching in Linear Space Technical University of Denmark, Denmark
July 2-4 2014
• ARCO Workshop
Malmö University, Sweden
April 25 2014
Presented Fingerprints in Compressed Strings University of Western Ontario, Canada
August 12-14 2013
• CPM 2013
June 17-19 2013
• ARCO Workshop
Gave a talk on String Matching with Fingerprints
SDU Odense, Denmark
April 5 2013
• Storage & Indexing of Massive Data
The Royal Society at Chicheley Hall, Buckinghamshire, UK
February 7-8 2013
• ARCO Workshop
IT University, Denmark
November 15 2012
• CPM 2012 / SWAT 2012
University of Helsinki, Finland
July 3-6 2012

• External research visit with Benjamin Sach
University of Bristol, UK
August 31 - October 3 2014
• External research visit with Roberto Grossi
Gave a talk on Fingerprints in Compressed Strings University of Pisa, Italy
January 7 - April 10 2014
• Invited visit hosted by Raphael Clifford
University of Bristol, UK
November 15-22 2013
• Invited visit hosted by Benjamin Sach
University of Warwick, UK
February 4-6 2013
• Erasmus Intensive Programme: DOSSEE 2011