Gerth Stølting Brodal

Bio: Gerth Stølting Brodal is an academic researcher from Aarhus University. The author has contributed to research in topics: Data structure & Priority queue. The author has an hindex of 39, co-authored 166 publications receiving 4420 citations. Previous affiliations of Gerth Stølting Brodal include National Research Foundation of South Africa & Max Planck Society.

Strictly Implicit Priority Queues: On the Number of Moves and Worst-Case Time

Abstract: The binary heap of Williams (1964) is a simple priority queue characterized by only storing an array containing the elements and the number of elements $n$ - here denoted a strictly implicit priority queue. We introduce two new strictly implicit priority queues. The first structure supports amortized $O(1)$ time Insert and $O(\log n)$ time ExtractMin operations, where both operations require amortized $O(1)$ element moves. No previous implicit heap with $O(1)$ time Insert supports both operations with $O(1)$ moves. The second structure supports worst-case $O(1)$ time Insert and $O(\log n)$ time (and moves) ExtractMin operations. Previous results were either amortized or needed $O(\log n)$ bits of additional state information between operations.

External Memory Three-Sided Range Reporting and Top-$k$ Queries with Sublogarithmic Updates

Abstract: An external memory data structure is presented for maintaining a dynamic set of $N$ two-dimensional points under the insertion and deletion of points, and supporting 3-sided range reporting queries and top-$k$ queries, where top-$k$ queries report the $k$~points with highest $y$-value within a given $x$-range. For any constant $0<\varepsilon\leq \frac{1}{2}$, a data structure is constructed that supports updates in amortized $O(\frac{1}{\varepsilon B^{1-\varepsilon}}\log_B N)$ IOs and queries in amortized $O(\frac{1}{\varepsilon}\log_B N+K/B)$ IOs, where $B$ is the external memory block size, and $K$ is the size of the output to the query (for top-$k$ queries $K$ is the minimum of $k$ and the number of points in the query interval). The data structure uses linear space. The update bound is a significant factor $B^{1-\varepsilon}$ improvement over the previous best update bounds for the two query problems, while staying within the same query and space bounds.

Cache-Oblivious Sorting

Abstract: In the cache-oblivious setting, the computational model is a machine with two levels of memory: a cache of limited capacity and a secondary memory of infinite capacity. The capacity of the cache is assumed to be M elements, and data is moved between the two levels of memory in blocks of B consecutive elements. Computations can only be performed on elements stored in cache, i.e., elements from secondary memory need to be moved to the cache before operations can access the elements. Programs are written as acting directly on one unbounded memory, i.e., programs are like standard RAM programs. The necessary block transfers between cache and secondary memory are handled automatically by the model, assuming an optimal offline cache replacement strategy. The core assumption of the cache-oblivious model is that M and B are unknown to the algorithm, whereas in the related I/O model introduced by Aggarwal and Vitter [1], the algorithms know M and B , and the algorithms perform the block transfers explicitly. A thorough discussion of the cache-oblivious model and its relation to multilevel memory hierarchies is given in [8].

External Memory Fully Persistent Search Trees

Abstract: We present the first fully-persistent external-memory search tree achieving amortized I/O bounds matching those of the classic (ephemeral) B-tree by Bayer and McCreight. The insertion and deletion of a value in any version requires amortized O(logB Nv) I/Os and a range reporting query in any version requires worst-case O(logB Nv + K/B) I/Os, where K is the number of values reported, Nv is the number of values in the version v of the tree queried or updated, and B is the external-memory block size. The data structure requires space linear in the total number of updates. Compared to the previous best bounds for fully persistent B-trees [Brodal, Sioutas, Tsakalidis, and Tsichlas, SODA 2012], this paper eliminates from the update bound an additive term of O(log2 B) I/Os. This result matches the previous best bounds for the restricted case of partial persistent B-trees [Arge, Danner and Teh, JEA 2003]. Central to our approach is to consider the problem as a dynamic set of two-dimensional rectangles that can be merged and split.

D$^2$-Tree: A New Overlay with Deterministic Bounds

Abstract: We present a new overlay, called the {\em Deterministic Decentralized tree} ($D^2$-tree). The $D^2$-tree compares favourably to other overlays for the following reasons: (a) it provides matching and better complexities, which are deterministic for the supported operations; (b) the management of nodes (peers) and elements are completely decoupled from each other; and (c) an efficient deterministic load-balancing mechanism is presented for the uniform distribution of elements into nodes, while at the same time probabilistic optimal bounds are provided for the congestion of operations at the nodes. The load-balancing scheme of elements into nodes is deterministic and general enough to be applied to other hierarchical tree-based overlays. This load-balancing mechanism is based on an innovative lazy weight-balancing mechanism, which is interesting in its own right.

Application of Phylogenetic Networks in Evolutionary Studies

Abstract: The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.

FastTree: Computing Large Minimum Evolution Trees with Profiles instead of a Distance Matrix

Abstract: Gene families are growing rapidly, but standard methods for inferring phylogenies do not scale to alignments with over 10,000 sequences. We present FastTree, a method for constructing large phylogenies and for estimating their reliability. Instead of storing a distance matrix, FastTree stores sequence profiles of internal nodes in the tree. FastTree uses these profiles to implement Neighbor-Joining and uses heuristics to quickly identify candidate joins. FastTree then uses nearest neighbor interchanges to reduce the length of the tree. For an alignment with N sequences, L sites, and a different characters, a distance matrix requires O(N2) space and O(N2L) time, but FastTree requires just O(NLa + N) memory and O(Nlog (N)La) time. To estimate the tree's reliability, FastTree uses local bootstrapping, which gives another 100-fold speedup over a distance matrix. For example, FastTree computed a tree and support values for 158,022 distinct 16S ribosomal RNAs in 17 h and 2.4 GB of memory. Just computing pairwise Jukes–Cantor distances and storing them, without inferring a tree or bootstrapping, would require 17 h and 50 GB of memory. In simulations, FastTree was slightly more accurate than Neighbor-Joining, BIONJ, or FastME; on genuine alignments, FastTree's topologies had higher likelihoods. FastTree is available at http://microbesonline.org/fasttree.

Fast Tree: Computing Large Minimum-Evolution Trees with Profiles instead of a Distance Matrix

Abstract: Gene families are growing rapidly, but standard methods for inferring phylogenies do not scale to alignments with over 10,000 sequences. We present FastTree, a method for constructing large phylogenies and for estimating their reliability. Instead of storing a distance matrix, FastTree stores sequence profiles of internal nodes in the tree. FastTree uses these profiles to implement neighbor-joining and uses heuristics to quickly identify candidate joins. FastTree then uses nearest-neighbor interchanges to reduce the length of the tree. For an alignment with N sequences, L sites, and a different characters, a distance matrix requires O(N^2) space and O(N^2 L) time, but FastTree requires just O( NLa + N sqrt(N) ) memory and O( N sqrt(N) log(N) L a ) time. To estimate the tree's reliability, FastTree uses local bootstrapping, which gives another 100-fold speedup over a distance matrix. For example, FastTree computed a tree and support values for 158,022 distinct 16S ribosomal RNAs in 17 hours and 2.4 gigabytes of memory. Just computing pairwise Jukes-Cantor distances and storing them, without inferring a tree or bootstrapping, would require 17 hours and 50 gigabytes of memory. In simulations, FastTree was slightly more accurate than neighbor joining, BIONJ, or FastME; on genuine alignments, FastTree's topologies had higher likelihoods. FastTree is available at http://microbesonline.org/fasttree.

BOLD : The Barcode of Life Data System (www.barcodinglife.org)

Abstract: The Barcode of Life Data System ( BOLD ) is an informatics workbench aiding the acquisition, storage, analysis and publication of DNA barcode records. By assembling molecular, morphological and distributional data, it bridges a traditional bioinformatics chasm. BOLD is freely available to any researcher with interests in DNA barcoding. By providing specialized services, it aids the assembly of records that meet the standards needed to gain BARCODE designation in the global sequence databases. Because of its web-based delivery and flexible data security model, it is also well positioned to support projects that involve broad research alliances. This paper provides a brief introduction to the key elements of BOLD , discusses their functional capabilities, and concludes by examining computational resources and future prospects.