eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
1
434
10.4230/LIPIcs.SEA.2021
article
LIPIcs, Volume 190, SEA 2021, Complete Volume
Coudert, David
1
https://orcid.org/0000-0002-3306-8314
Natale, Emanuele
2
https://orcid.org/0000-0002-8755-3892
I3S (CNRS-UCA)/Inria, Sophia Antipolis, France
Université Côte d’Azur, CNRS, France
LIPIcs, Volume 190, SEA 2021, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021/LIPIcs.SEA.2021.pdf
LIPIcs, Volume 190, SEA 2021, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
0:i
0:xii
10.4230/LIPIcs.SEA.2021.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Coudert, David
1
https://orcid.org/0000-0002-3306-8314
Natale, Emanuele
2
https://orcid.org/0000-0002-8755-3892
I3S (CNRS-UCA)/Inria, Sophia Antipolis, France
Université Côte d’Azur, CNRS, France
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.0/LIPIcs.SEA.2021.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
1:1
1:18
10.4230/LIPIcs.SEA.2021.1
article
Engineering Nearly Linear-Time Algorithms for Small Vertex Connectivity
Franck, Max
1
https://orcid.org/0000-0003-3583-8033
Yingchareonthawornchai, Sorrachai
1
https://orcid.org/0000-0002-7169-0163
Department of Computer Science, Aalto University, Espoo, Finland
Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is k-connected if it remains connected after removing any k-1 vertices. The vertex connectivity of a graph is the maximum k such that the graph is k-connected. There is a long history of algorithmic development for efficiently computing vertex connectivity. Recently, two near linear-time algorithms for small k were introduced by [Forster et al. SODA 2020]. Prior to that, the best known algorithm was one by [Henzinger et al. FOCS'96] with quadratic running time when k is small.
In this paper, we study the practical performance of the algorithms by Forster et al. In addition, we introduce a new heuristic on a key subroutine called local cut detection, which we call degree counting. We prove that the new heuristic improves space-efficiency (which can be good for caching purposes) and allows the subroutine to terminate earlier. According to experimental results on random graphs with planted vertex cuts, random hyperbolic graphs, and real world graphs with vertex connectivity between 4 and 15, the degree counting heuristic offers a factor of 2-4 speedup over the original non-degree counting version for most of our data. It also outperforms the previous state-of-the-art algorithm by Henzinger et al. even on relatively small graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.1/LIPIcs.SEA.2021.1.pdf
Algorithm Engineering
Algorithmic Graph Theory
Sublinear Algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
2:1
2:18
10.4230/LIPIcs.SEA.2021.2
article
Parallel Five-Cycle Counting Algorithms
Huang, Louisa Ruixue
1
Shi, Jessica
1
Shun, Julian
1
MIT, CSAIL, Cambridge, MA, USA
Counting the frequency of subgraphs in large networks is a classic research question that reveals the underlying substructures of these networks for important applications. However, subgraph counting is a challenging problem, even for subgraph sizes as small as five, due to the combinatorial explosion in the number of possible occurrences. This paper focuses on the five-cycle, which is an important special case of five-vertex subgraph counting and one of the most difficult to count efficiently.
We design two new parallel five-cycle counting algorithms and prove that they are work-efficient and achieve polylogarithmic span. Both algorithms are based on computing low out-degree orientations, which enables the efficient computation of directed two-paths and three-paths, and the algorithms differ in the ways in which they use this orientation to eliminate double-counting. We develop fast multicore implementations of the algorithms and propose a work scheduling optimization to improve their performance. Our experiments on a variety of real-world graphs using a 36-core machine with two-way hyper-threading show that our algorithms achieves 10-46x self-relative speed-up, outperform our serial benchmarks by 10-32x, and outperform the previous state-of-the-art serial algorithm by up to 818x.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.2/LIPIcs.SEA.2021.2.pdf
Cycle counting
parallel algorithms
graph algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
3:1
3:16
10.4230/LIPIcs.SEA.2021.3
article
Fast and Robust Vectorized In-Place Sorting of Primitive Types
Blacher, Mark
1
Giesen, Joachim
1
Kühne, Lars
2
Institute for Theoretical Computer Science, Friedrich Schiller Universität Jena, Germany
German Aerospace Center (DLR), Jena, Germany
Modern CPUs provide single instruction-multiple data (SIMD) instructions. SIMD instructions process several elements of a primitive data type simultaneously in fixed-size vectors. Classical sorting algorithms are not directly expressible in SIMD instructions. Accelerating sorting algorithms with SIMD instruction is therefore a creative endeavor. A promising approach for sorting with SIMD instructions is to use sorting networks for small arrays and Quicksort for large arrays. In this paper we improve vectorization techniques for sorting networks and Quicksort. In particular, we show how to use the full capacity of vector registers in sorting networks and how to make vectorized Quicksort robust with respect to different key distributions. To demonstrate the performance of our techniques we implement an in-place hybrid sorting algorithm for the data type int with AVX2 intrinsics. Our implementation is at least 30% faster than state-of-the-art high-performance sorting alternatives.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.3/LIPIcs.SEA.2021.3.pdf
Quicksort
Sorting Networks
Vectorization
SIMD
AVX2
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
4:1
4:16
10.4230/LIPIcs.SEA.2021.4
article
Minimum Scan Cover and Variants - Theory and Experiments
Buchin, Kevin
1
https://orcid.org/0000-0002-3022-7877
Fekete, Sándor P.
2
https://orcid.org/0000-0002-9062-4241
Hill, Alexander
2
https://orcid.org/0000-0002-9270-9871
Kleist, Linda
2
https://orcid.org/0000-0002-3786-916X
Kostitsyna, Irina
1
https://orcid.org/0000-0003-0544-2257
Krupke, Dominik
2
https://orcid.org/0000-0003-1573-3496
Lambers, Roel
1
https://orcid.org/0000-0002-0314-6094
Struijs, Martijn
1
https://orcid.org/0000-0002-0116-7238
Department of Mathematics & Computer Science, TU Eindhoven, The Netherlands
Department of Computer Science, TU Braunschweig, Germany
We consider a spectrum of geometric optimization problems motivated by contexts such as satellite communication and astrophysics. In the problem Minimum Scan Cover with Angular Costs, we are given a graph G that is embedded in Euclidean space. The edges of G need to be scanned, i.e., probed from both of their vertices. In order to scan their edge, two vertices need to face each other; changing the heading of a vertex incurs some cost in terms of energy or rotation time that is proportional to the corresponding rotation angle. Our goal is to compute schedules that minimize the following objective functions: (i) in Minimum Makespan Scan Cover (MSC-MS), this is the time until all edges are scanned; (ii) in Minimum Total Energy Scan Cover (MSC-TE), the sum of all rotation angles; (iii) in Minimum Bottleneck Energy Scan Cover (MSC-BE), the maximum total rotation angle at one vertex.
Previous theoretical work on MSC-MS revealed a close connection to graph coloring and the cut cover problem, leading to hardness and approximability results. In this paper, we present polynomial-time algorithms for 1D instances of MSC-TE and MSC-BE, but NP-hardness proofs for bipartite 2D instances. For bipartite graphs in 2D, we also give 2-approximation algorithms for both MSC-TE and MSC-BE. Most importantly, we provide a comprehensive study of practical methods for all three problems. We compare three different mixed-integer programming and two constraint programming approaches, and show how to compute provably optimal solutions for geometric instances with up to 300 edges. Additionally, we compare the performance of different meta-heuristics for even larger instances.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.4/LIPIcs.SEA.2021.4.pdf
Graph scanning
angular metric
makespan
energy
bottleneck
complexity
approximation
algorithm engineering
mixed-integer programming
constraint programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
5:1
5:15
10.4230/LIPIcs.SEA.2021.5
article
Three Is Enough for Steiner Trees
Arrighi, Emmanuel
1
https://orcid.org/0000-0002-0326-1893
de Oliveira Oliveira, Mateus
1
https://orcid.org/0000-0001-7798-7446
University of Bergen, Norway
In the Steiner tree problem, the input consists of an edge-weighted graph G together with a set S of terminal vertices. The goal is to find a minimum weight tree in G that spans all terminals. This fundamental NP-hard problem has direct applications in many subfields of combinatorial optimization, such as planning, scheduling, etc. In this work we introduce a new heuristic for the Steiner tree problem, based on a simple routine for improving the cost of sub-optimal Steiner trees: first, the sub-optimal tree is split into three connected components, and then these components are reconnected by using an algorithm that computes an optimal Steiner tree with 3-terminals (the roots of the three components). We have implemented our heuristic into a solver and compared it with several state-of-the-art solvers on well-known data sets. Our solver performs very well across all the data sets, and outperforms most of the other benchmarked solvers on very large graphs, which have been either obtained from real-world applications or from randomly generated data sets.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.5/LIPIcs.SEA.2021.5.pdf
Steiner Tree
Heuristics
3TST
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
6:1
6:16
10.4230/LIPIcs.SEA.2021.6
article
A Fast and Tight Heuristic for A* in Road Networks
Strasser, Ben
1
Zeitz, Tim
2
https://orcid.org/0000-0003-4746-3582
Stuttgart, Germany
Karlsruhe Institute of Technology, Germany
We study exact, efficient and practical algorithms for route planning in large road networks. Routing applications often require integrating the current traffic situation, planning ahead with traffic predictions for the future, respecting forbidden turns, and many other features depending on the exact application. While Dijkstra’s algorithm can be used to solve these problems, it is too slow for many applications. A* is a classical approach to accelerate Dijkstra’s algorithm. A* can support many extended scenarios without much additional implementation complexity. However, A*’s performance depends on the availability of a good heuristic that estimates distances. Computing tight distance estimates is a challenge on its own. On road networks, shortest paths can also be quickly computed using hierarchical speedup techniques. They achieve speed and exactness but sacrifice A*’s flexibility. Extending them to certain practical applications can be hard. In this paper, we present an algorithm to efficiently extract distance estimates for A* from Contraction Hierarchies (CH), a hierarchical technique. We call our heuristic CH-Potentials. Our approach allows decoupling the supported extensions from the hierarchical speed-up technique. Additionally, we describe A* optimizations to accelerate the processing of low degree nodes, which often occur in road networks.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.6/LIPIcs.SEA.2021.6.pdf
route planning
shortest paths
realistic road networks
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
7:1
7:19
10.4230/LIPIcs.SEA.2021.7
article
Engineering Predecessor Data Structures for Dynamic Integer Sets
Dinklage, Patrick
1
https://orcid.org/0000-0002-2004-6781
Fischer, Johannes
1
Herlez, Alexander
1
TU Dortmund University, Germany
We present highly optimized data structures for the dynamic predecessor problem, where the task is to maintain a set S of w-bit numbers under insertions, deletions, and predecessor queries (return the largest element in S no larger than a given key). The problem of finding predecessors can be viewed as a generalized form of the membership problem, or as a simple version of the nearest neighbour problem. It lies at the core of various real-world problems such as internet routing.
In this work, we engineer (1) a simple implementation of the idea of universe reduction, similar to van-Emde-Boas trees (2) variants of y-fast tries [Willard, IPL'83], and (3) B-trees with different strategies for organizing the keys contained in the nodes, including an implementation of dynamic fusion nodes [Pǎtraşcu and Thorup, FOCS'14]. We implement our data structures for w = 32,40,64, which covers most typical scenarios.
Our data structures finish workloads faster than previous approaches while being significantly more space-efficient, e.g., they clearly outperform standard implementations of the STL by finishing up to four times as fast using less than a third of the memory. Our tests also provide more general insights on data structure design, such as how small sets should be stored and handled and if and when new CPU instructions such as advanced vector extensions pay off.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.7/LIPIcs.SEA.2021.7.pdf
integer data structures
dynamic data structures
predecessor
universe reduction
y-fast trie
fusion tree
B-tree
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
8:1
8:20
10.4230/LIPIcs.SEA.2021.8
article
Multilevel Hypergraph Partitioning with Vertex Weights Revisited
Heuer, Tobias
1
Maas, Nikolai
1
Schlag, Sebastian
1
Karlsruhe Institute of Technology, Germany
The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications often use vertex and edge weights to accurately model the underlying problem, the HGP research community commonly works with unweighted instances.
In this paper, we argue that, in the presence of vertex weights, current balance constraint definitions either yield infeasible partitioning problems or allow unnecessarily large imbalances and propose a new definition that overcomes these problems. We show that state-of-the-art hypergraph partitioners often struggle considerably with weighted instances and tight balance constraints (even with our new balance definition). Thus, we present a recursive-bipartitioning technique that is able to reliably compute balanced (and hence feasible) solutions. The proposed method balances the partition by pre-assigning a small subset of the heaviest vertices to the two blocks of each bipartition (using an algorithm originally developed for the job scheduling problem) and optimizes the actual partitioning objective on the remaining vertices. We integrate our algorithm into the multilevel hypergraph partitioner KaHyPar and show that our approach is able to compute balanced partitions of high quality on a diverse set of benchmark instances.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.8/LIPIcs.SEA.2021.8.pdf
multilevel hypergraph partitioning
balanced partitioning
vertex weights
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
9:1
9:18
10.4230/LIPIcs.SEA.2021.9
article
On Tamaki’s Algorithm to Compute Treewidths
Althaus, Ernst
1
https://orcid.org/0000-0002-2122-9520
Schnurbusch, Daniela
1
Wüschner, Julian
1
Ziegler, Sarah
1
Johannes Gutenberg-Universität Mainz, Germany
We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.9/LIPIcs.SEA.2021.9.pdf
Tree Decomposition
Exact Algorithm
Algorithms Engineering
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
10:1
10:13
10.4230/LIPIcs.SEA.2021.10
article
Practical Implementation of Encoding Range Top-2 Queries
Jo, Seungbum
1
Park, Wooyoung
2
Satti, Srinivasa Rao
3
Chungbuk National University, Cheongju, South Korea
Seoul National University, South Korea
Norwegian University of Science and Technology, Trondheim, Norway
We design a practical variant of an encoding for range Top-2 queries (RT2Q), and evaluate its performance. Given an array A[1,n] of n elements from a total order, the range Top-2 encoding problem is to construct a data structure that can answer RT2Q queries, which return the positions of the first and the second largest elements within a given query range of A, without accessing the array A at query time. Davoodi et al. [Phil. Trans. Royal Soc. A, 2016] proposed a (3.272n + o(n))-bit encoding, which answers RT2Q queries in O(1) time, while Gawrychowski and Nicholson [ICALP, 2015] gave an optimal (2.755n + (n))-bit encoding which doesn't support efficient queries. In this paper, we propose the first practical implementation of the encoding data structure for answering RT2Q. Our implementation is based on an alternative representation of Davoodi et al.’s data structure. The experimental results show that our implementation is efficient in practice, and gives improved time-space trade-offs compared to the indexing data structures (which keep the original array A as part of the data structure) for range maximum queries.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.10/LIPIcs.SEA.2021.10.pdf
Range top-2 query
Range minimum query
Cartesian tree
Succinct encoding
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
11:1
11:21
10.4230/LIPIcs.SEA.2021.11
article
On Computing the Diameter of (Weighted) Link Streams
Calamai, Marco
1
Crescenzi, Pierluigi
2
Marino, Andrea
1
University of Florence, Italy
Gran Sasso Science Institute, L'Aquila, Italy
A weighted link stream is a pair (V,𝔼) comprising V, the set of nodes, and 𝔼, the list of temporal edges (u,v,t,λ), where u,v are two nodes in V, t is the starting time of the temporal edge, and λ is its travel time. By making use of this model, different notions of diameter can be defined, which refer to the following distances: earliest arrival time, latest departure time, fastest time, and shortest time. After proving that any of these diameters cannot be computed in time sub-quadratic with respect to the number of temporal edges, we propose different algorithms (inspired by the approach used for computing the diameter of graphs) which allow us to compute, in practice very efficiently, the diameter of quite large real-world weighted link stream for several definitions of the diameter. Indeed, all the proposed algorithms require very often a very low number of single source (or target) best path computations. We verify the effectiveness of our approach by means of an extensive set of experiments on real-world link streams. We also experimentally prove that the temporal version of the well-known 2-sweep technique, for computing a lower bound on the diameter of a graph, is quite effective in the case of weighted link stream, by returning very often tight bounds.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.11/LIPIcs.SEA.2021.11.pdf
Temporal graph
shortest path
diameter
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
12:1
12:12
10.4230/LIPIcs.SEA.2021.12
article
Document Retrieval Hacks
Puglisi, Simon J.
1
Zhukova, Bella
1
Department of Computer Science, University of Helsinki, Finland
Given a collection of strings, document listing refers to the problem of finding all the strings (or documents) where a given query string (or pattern) appears. Index data structures that support efficient document listing for string collections have been the focus of intense research in the last decade, with dozens of papers published describing exotic and elegant compressed data structures. The problem is now quite well understood in theory and many of the solutions have been implemented and evaluated experimentally. A particular recent focus has been on highly repetitive document collections, which have become prevalent in many areas (such as version control systems and genomics - to name just two very different sources).
The aim of this paper is to describe simple and efficient document listing algorithms that can be used in combination with more sophisticated techniques, or as baselines against which the performance of new document listing indexes can be measured. Our approaches are based on simple combinations of scanning and hashing, which we show to combine very well with dictionary compression to achieve small space usage. Our experiments show these methods to be often much faster and less space consuming than the best specialized indexes for the problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.12/LIPIcs.SEA.2021.12.pdf
String Processing
Pattern matching
Document listing
Document retrieval
Succinct data structures
Repetitive text collections
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
13:1
13:24
10.4230/LIPIcs.SEA.2021.13
article
O'Reach: Even Faster Reachability in Large Graphs
Hanauer, Kathrin
1
https://orcid.org/0000-0002-5945-837X
Schulz, Christian
2
https://orcid.org/0000-0002-2823-3506
Trummer, Jonathan
1
https://orcid.org/0000-0002-1086-4756
University of Vienna, Faculty of Computer Science, Austria
Heidelberg University, Germany
One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support a large portion of reachability queries in constant time using a linear-sized reachability index. Our new algorithm O'Reach can be easily combined with previously developed solutions for the problem or run standalone.
In a detailed experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint on a diverse set of instances. Our experiments indicate that the query performance often depends strongly not only on the type of graph, but also on the result, i.e., reachable or unreachable. Furthermore, we show that previous algorithms are significantly sped up when combined with our new approach in almost all scenarios. Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even faster than single memory accesses in a precomputed full reachability matrix.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.13/LIPIcs.SEA.2021.13.pdf
Reachability
Static Graphs
Graph Algorithms
Reachability Index
Algorithm Engineering
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
14:1
14:19
10.4230/LIPIcs.SEA.2021.14
article
Approximation Algorithms for 1-Wasserstein Distance Between Persistence Diagrams
Chen, Samantha
1
Wang, Yusu
1
University of California at San Diego, La Jolla, CA, USA
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially complex input object (be it a graph, an image, or a point set and so on) to a unified type of feature summary, called the persistence diagrams. One can then carry out downstream data analysis tasks using such persistence diagram representations. A key problem is to compute the distance between two persistence diagrams efficiently. In particular, a persistence diagram is essentially a multiset of points in the plane, and one popular distance is the so-called 1-Wasserstein distance between persistence diagrams. In this paper, we present two algorithms to approximate the 1-Wasserstein distance for persistence diagrams in near-linear time. These algorithms primarily follow the same ideas as two existing algorithms to approximate optimal transport between two finite point-sets in Euclidean spaces via randomly shifted quadtrees. We show how these algorithms can be effectively adapted for the case of persistence diagrams. Our algorithms are much more efficient than previous exact and approximate algorithms, both in theory and in practice, and we demonstrate its efficiency via extensive experiments. They are conceptually simple and easy to implement, and the code is publicly available in github.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.14/LIPIcs.SEA.2021.14.pdf
persistence diagrams
approximation algorithms
Wasserstein distance
optimal transport
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
15:1
15:16
10.4230/LIPIcs.SEA.2021.15
article
Fréchet Mean and p-Mean on the Unit Circle: Decidability, Algorithm, and Applications to Clustering on the Flat Torus
Cazals, Frédéric
1
2
Delmas, Bernard
3
O'Donnell, Timothee
1
2
Université Côte d'Azur, France
Inria, Sophia Antipolis, France
INRAe, Jouy-en-Josas, France
The center of mass of a point set lying on a manifold generalizes the celebrated Euclidean centroid, and is ubiquitous in statistical analysis in non Euclidean spaces. In this work, we give a complete characterization of the weighted p-mean of a finite set of angular values on S¹, based on a decomposition of S¹ such that the functional of interest has at most one local minimum per cell. This characterization is used to show that the problem is decidable for rational angular values -a consequence of Lindemann’s theorem on the transcendence of π, and to develop an effective algorithm parameterized by exact predicates. A robust implementation of this algorithm based on multi-precision interval arithmetic is also presented, and is shown to be effective for large values of n and p. We use it as building block to implement the k-means and k-means++ clustering algorithms on the flat torus, with applications to clustering protein molecular conformations. These algorithms are available in the Structural Bioinformatics Library (http://sbl.inria.fr).
Our derivations are of interest in two respects. First, efficient p-mean calculations are relevant to develop principal components analysis on the flat torus encoding angular spaces-a particularly important case to describe molecular conformations. Second, our two-stage strategy stresses the interest of combinatorial methods for p-means, also emphasizing the role of numerical issues.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.15/LIPIcs.SEA.2021.15.pdf
Frechét mean
p-mean
circular statistics
decidability
robustness
multi-precision
angular spaces
flat torus
clustering
molecular conformations
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
16:1
16:23
10.4230/LIPIcs.SEA.2021.16
article
Multi-Level Weighted Additive Spanners
Ahmed, Reyan
1
Bodwin, Greg
2
Sahneh, Faryad Darabi
1
Hamm, Keaton
3
Kobourov, Stephen
1
Spence, Richard
1
University of Arizona, Tucson, AZ, USA
University of Michigan, Ann Arbor, MI, USA
University of Texas at Arlington, TX, USA
Given a graph G = (V,E), a subgraph H is an additive +β spanner if dist_H(u,v) ≤ dist_G(u,v) + β for all u, v ∈ V. A pairwise spanner is a spanner for which the above inequality is only required to hold for specific pairs P ⊆ V × V given on input; when the pairs have the structure P = S × S for some S ⊆ V, it is called a subsetwise spanner. Additive spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs.
In this paper, we consider a multi-level version of the subsetwise additive spanner in weighted graphs motivated by multi-level network design and visualization, where the vertices in S possess varying level, priority, or quality of service (QoS) requirements. The goal is to compute a nested sequence of spanners with the minimum total number of edges. We first generalize the +2 subsetwise spanner of [Pettie 2008, Cygan et al., 2013] to the weighted setting. We experimentally measure the performance of this and several existing algorithms by [Ahmed et al., 2020] for weighted additive spanners, both in terms of runtime and sparsity of the output spanner, when applied as a subroutine to multi-level problem.
We provide an experimental evaluation on graphs using several different random graph generators and show that these spanner algorithms typically achieve much better guarantees in terms of sparsity and additive error compared with the theoretical maximum. By analyzing our experimental results, we additionally developed a new technique of changing a certain initialization parameter which provides better spanners in practice at the expense of a small increase in running time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.16/LIPIcs.SEA.2021.16.pdf
multi-level
graph spanner
approximation algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
17:1
17:21
10.4230/LIPIcs.SEA.2021.17
article
Targeted Branching for the Maximum Independent Set Problem
Hespe, Demian
1
https://orcid.org/0000-0001-6232-2951
Lamm, Sebastian
1
https://orcid.org/0000-0001-7828-921X
Schorr, Christian
1
Karlsruhe Institute of Technology, Institute for Theoretical Informatics, Germany
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm.
In this work, we develop and evaluate several novel branching strategies for both branch-and-bound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.17/LIPIcs.SEA.2021.17.pdf
Graphs
Combinatorial Optimization
Independent Set
Vertex Cover
Clique
Branch-and-Reduce
Branch-and-Bound
Data Reduction
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
18:1
18:18
10.4230/LIPIcs.SEA.2021.18
article
Nearest-Neighbor Queries in Customizable Contraction Hierarchies and Applications
Buchhold, Valentin
1
Wagner, Dorothea
1
Karlsruhe Institute of Technology, Germany
Customizable contraction hierarchies are one of the most popular route planning frameworks in practice, due to their simplicity and versatility. In this work, we present a novel algorithm for finding k-nearest neighbors in customizable contraction hierarchies by systematically exploring the associated separator decomposition tree. Compared to previous bucket-based approaches, our algorithm requires much less target-dependent preprocessing effort. Moreover, we use our novel approach in two concrete applications. The first application are online k-closest point-of-interest queries, where the points of interest are only revealed at query time. We achieve query times of about 25 milliseconds on a continental road network, which is fast enough for interactive systems. The second application is travel demand generation. We show how to accelerate a recently introduced travel demand generator by a factor of more than 50 using our novel nearest-neighbor algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.18/LIPIcs.SEA.2021.18.pdf
Nearest neighbors
points of interest
travel demand generation
radiation model
customizable contraction hierarchies
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
19:1
19:18
10.4230/LIPIcs.SEA.2021.19
article
A Graph-Based Similarity Approach to Classify Recurrent Complex Motifs from Their Context in RNA Structures
Gianfrotta, Coline
1
2
https://orcid.org/0000-0001-5792-4966
Reinharz, Vladimir
3
https://orcid.org/0000-0001-8481-1094
Barth, Dominique
1
Denise, Alain
2
4
https://orcid.org/0000-0003-4484-4996
Université de Versailles Saint-Quentin-en-Yvelines, Université Paris-Saclay, DAVID lab, France
Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400, Orsay, France
Department of Computer Science, Université du Québec à Montréal, Québec, Canada
Université Paris-Saclay, CNRS, I2BC, 91400, Orsay, France
This article proposes to use an RNA graph similarity metric, based on the MCES resolution problem, to compare the occurrences of specific complex motifs in RNA graphs, according to their context represented as subgraph. We rely on a new modeling by graphs of these contexts, at two different levels of granularity, and obtain a classification of these graphs, which is consistent with the RNA 3D structure.
RNA many non-translational functions, as a ribozyme, riboswitch, or ribosome, require complex structures. Those are composed of a rigid skeleton, a set of canonical interactions called the secondary structure. Decades of experimental and theoretical work have produced precise thermodynamic parameters and efficient algorithms to predict, from sequence, the secondary structure of RNA molecules. On top of the skeleton, the nucleotides form an intricate network of interactions that are not captured by present thermodynamic models. This network has been shown to be composed of modular motifs, that are linked to function, and have been leveraged for better prediction and design. A peculiar subclass of complex structural motifs are those connecting RNA regions far away in the secondary structure. They are crucial to predict since they determine the global shape of the molecule, therefore important for the function.
In this paper, we show by using our graph approach that the context is important for the formation of conserved complex structural motifs. We furthermore show that a natural classification of structural variants of the motifs emerges from their context. We explore the cases of three known motif families and we exhibit their experimentally emerging classification.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.19/LIPIcs.SEA.2021.19.pdf
Graph similarity
clustering
RNA 3D folding
RNA motif
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
20:1
20:19
10.4230/LIPIcs.SEA.2021.20
article
Computing Vertex-Edge Cut-Pairs and 2-Edge Cuts in Practice
Georgiadis, Loukas
1
https://orcid.org/0000-0002-9706-7409
Giannis, Konstantinos
2
Italiano, Giuseppe F.
3
https://orcid.org/0000-0002-9492-9894
Kosinas, Evangelos
1
Department of Computer Science & Engineering, University of Ioannina, Greece
Gran Sasso Science Institute, L'Aquila, Italy
LUISS University, Rome, Italy
We consider two problems regarding the computation of connectivity cuts in undirected graphs, namely identifying vertex-edge cut-pairs and identifying 2-edge cuts, and present an experimental study of efficient algorithms for their computation. In the first problem, we are given a biconnected graph G and our goal is to find all vertices v such that G⧵v is not 2-edge-connected, while in the second problem, we are given a 2-edge-connected graph G and our goal is to find all edges e such that G⧵e is not 2-edge-connected. These problems are motivated by the notion of twinless strong connectivity in directed graphs but are also of independent interest. Moreover, the computation of 2-edge cuts is a main step in algorithms that compute the 3-edge-connected components of a graph. In this paper, we present streamlined versions of two recent linear-time algorithms of Georgiadis and Kosinas that compute all vertex-edge cut-pairs and all 2-edge cuts, respectively. We compare the empirical performance of our vertex-edge cut-pairs algorithm with an alternative linear-time method that exploits the structure of the triconnected components of G. Also, we compare the empirical performance of our 2-edge cuts algorithm with the algorithm of Tsin, which was reported to be the fastest one among the previously existing for this problem. To that end, we conduct a thorough experimental study to highlight the merits and weaknesses of each technique.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.20/LIPIcs.SEA.2021.20.pdf
2-Connectivity
Graph Algorithms
Split Components
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
21:1
21:12
10.4230/LIPIcs.SEA.2021.21
article
How to Find the Exit from a 3-Dimensional Maze
Hermann, Miki
1
https://orcid.org/0000-0003-2517-2127
LIX, CNRS, École Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
We present several experimental algorithms for fast computation of variadic polynomials over non-negative integers.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.21/LIPIcs.SEA.2021.21.pdf
Young tableaux
randomized algorithm
probabilistic algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
22:1
22:18
10.4230/LIPIcs.SEA.2021.22
article
Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane
Bläsius, Thomas
1
Friedrich, Tobias
2
https://orcid.org/0000-0003-0076-6308
Katzmann, Maximilian
2
https://orcid.org/0000-0002-9302-5527
Karlsruhe Institute of Technology, Germany
Hasso Plattner Institute, University of Potsdam, Germany
Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness.
We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.22/LIPIcs.SEA.2021.22.pdf
force-directed drawing algorithms
spring embedding
hyperbolic space
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-05-31
190
23:1
23:23
10.4230/LIPIcs.SEA.2021.23
article
An Experimental Study of External Memory Algorithms for Connected Components
Brodal, Gerth Stølting
1
Fagerberg, Rolf
2
Hammer, David
3
2
Meyer, Ulrich
3
Penschuck, Manuel
3
Tran, Hung
3
Aarhus University, Denmark
University of Southern Denmark, Odense, Denmark
Goethe Universität Frankfurt, Germany
We empirically investigate algorithms for solving Connected Components in the external memory model. In particular, we study whether the randomized O(Sort(E)) algorithm by Karger, Klein, and Tarjan can be implemented to compete with practically promising and simpler algorithms having only slightly worse theoretical cost, namely Borůvka’s algorithm and the algorithm by Sibeyn and collaborators. For all algorithms, we develop and test a number of tuning options. Our experiments are executed on a large set of different graph classes including random graphs, grids, geometric graphs, and hyperbolic graphs. Among our findings are: The Sibeyn algorithm is a very strong contender due to its simplicity and due to an added degree of freedom in its internal workings when used in the Connected Components setting. With the right tunings, the Karger-Klein-Tarjan algorithm can be implemented to be competitive in many cases. Higher graph density seems to benefit Karger-Klein-Tarjan relative to Sibeyn. Borůvka’s algorithm is not competitive with the two others.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol190-sea2021/LIPIcs.SEA.2021.23/LIPIcs.SEA.2021.23.pdf
Connected Components
Experimental Evaluation
External Memory
Graph Algorithms
Randomization