Volume
LIPIcs, Volume 265
21st International Symposium on Experimental Algorithms (SEA 2023)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Experimental Algorithms (SEA)
Event
SEA 2023, July 24-26, 2023, Barcelona, SpainEditor
Publication Details
- published at: 2023-07-19
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-279-2
- DBLP: db/conf/wea/sea2023
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Complete Volume
LIPIcs, Volume 265, SEA 2023, Complete Volume
Abstract
LIPIcs, Volume 265, SEA 2023, Complete Volume
Cite as
21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 1-390, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@Proceedings{georgiadis:LIPIcs.SEA.2023,
title = {{LIPIcs, Volume 265, SEA 2023, Complete Volume}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {1--390},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023},
URN = {urn:nbn:de:0030-drops-183495},
doi = {10.4230/LIPIcs.SEA.2023},
annote = {Keywords: LIPIcs, Volume 265, SEA 2023, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{georgiadis:LIPIcs.SEA.2023.0,
author = {Georgiadis, Loukas},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {0:i--0:xii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.0},
URN = {urn:nbn:de:0030-drops-183508},
doi = {10.4230/LIPIcs.SEA.2023.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Engineering a Preprocessor for Symmetry Detection
Abstract
State-of-the-art solvers for symmetry detection in combinatorial objects are becoming increasingly sophisticated software libraries. Most of the solvers were initially designed with inputs from combinatorics in mind (nauty, bliss, Traces, dejavu). They excel at dealing with a complicated core of the input. Others focus on practical instances that exhibit sparsity. They excel at dealing with comparatively easy but extremely large substructures of the input (saucy). In practice, these differences manifest in significantly diverging performances on different types of graph classes.
We engineer a preprocessor for symmetry detection. The result is a tool designed to shrink sparse, large substructures of the input graph. On most of the practical instances, the preprocessor improves the overall running time significantly for many of the state-of-the-art solvers. At the same time, our benchmarks show that the additional overhead is negligible.
Overall we obtain single algorithms with competitive performance across all benchmark graphs. As such, the preprocessor bridges the disparity between solvers that focus on combinatorial graphs and large practical graphs. In fact, on most of the practical instances the combined setup significantly outperforms previous state-of-the-art.
Cite as
Markus Anders, Pascal Schweitzer, and Julian Stieß. Engineering a Preprocessor for Symmetry Detection. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{anders_et_al:LIPIcs.SEA.2023.1,
author = {Anders, Markus and Schweitzer, Pascal and Stie{\ss}, Julian},
title = {{Engineering a Preprocessor for Symmetry Detection}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {1:1--1:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.1},
URN = {urn:nbn:de:0030-drops-183511},
doi = {10.4230/LIPIcs.SEA.2023.1},
annote = {Keywords: graph isomorphism, automorphism groups, symmetry detection, preprocessors}
}
Document
Fast Reachability Using DAG Decomposition
Abstract
We present a fast and practical algorithm to compute the transitive closure (TC) of a directed graph. It is based on computing a reachability indexing scheme of a directed acyclic graph (DAG), G = (V, E). Given any path/chain decomposition of G we show how to compute in parameterized linear time such a reachability scheme that can answer reachability queries in constant time. The experimental results reveal that our method is significantly faster in practice than the theoretical bounds imply, indicating that path/chain decomposition algorithms can be applied to obtain fast and practical solutions to the transitive closure (TC) problem. Furthermore, we show that the number of non-transitive edges of a DAG G is ≤ width*|V| and that we can find a substantially large subset of the transitive edges of G in linear time using a path/chain decomposition. Our extensive experimental results show the interplay between these concepts in various models of DAGs.
Cite as
Giorgos Kritikakis and Ioannis G. Tollis. Fast Reachability Using DAG Decomposition. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{kritikakis_et_al:LIPIcs.SEA.2023.2,
author = {Kritikakis, Giorgos and Tollis, Ioannis G.},
title = {{Fast Reachability Using DAG Decomposition}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {2:1--2:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.2},
URN = {urn:nbn:de:0030-drops-183526},
doi = {10.4230/LIPIcs.SEA.2023.2},
annote = {Keywords: graph algorithms, hierarchy, directed acyclic graphs (DAG), path/chain decomposition, transitive closure, transitive reduction, reachability, reachability indexing scheme}
}
Document
Partitioning the Bags of a Tree Decomposition into Cliques
Abstract
We consider a variant of treewidth that we call clique-partitioned treewidth in which each bag is partitioned into cliques. This is motivated by the recent development of FPT-algorithms based on similar parameters for various problems. With this paper, we take a first step towards computing clique-partitioned tree decompositions.
Our focus lies on the subproblem of computing clique partitions, i.e., for each bag of a given tree decomposition, we compute an optimal partition of the induced subgraph into cliques. The goal here is to minimize the product of the clique sizes (plus 1). We show that this problem is NP-hard. We also describe four heuristic approaches as well as an exact branch-and-bound algorithm. Our evaluation shows that the branch-and-bound solver is sufficiently efficient to serve as a good baseline. Moreover, our heuristics yield solutions close to the optimum. As a bonus, our algorithms allow us to compute first upper bounds for the clique-partitioned treewidth of real-world networks. A comparison to traditional treewidth indicates that clique-partitioned treewidth is a promising parameter for graphs with high clustering.
Cite as
Thomas Bläsius, Maximilian Katzmann, and Marcus Wilhelm. Partitioning the Bags of a Tree Decomposition into Cliques. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{blasius_et_al:LIPIcs.SEA.2023.3,
author = {Bl\"{a}sius, Thomas and Katzmann, Maximilian and Wilhelm, Marcus},
title = {{Partitioning the Bags of a Tree Decomposition into Cliques}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {3:1--3:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.3},
URN = {urn:nbn:de:0030-drops-183533},
doi = {10.4230/LIPIcs.SEA.2023.3},
annote = {Keywords: treewidth, weighted treewidth, algorithm engineering, cliques, clustering, complex networks}
}
Document
Subset Wavelet Trees
Abstract
Given an alphabet Σ of σ = |Σ| symbols, a degenerate (or indeterminate) string X is a sequence X = X[0],X[1]…, X[n-1] of n subsets of Σ. Since their introduction in the mid 70s, degenerate strings have been widely studied, with applications driven by their being a natural model for sequences in which there is a degree of uncertainty about the precise symbol at a given position, such as those arising in genomics and proteomics. In this paper we introduce a new data structural tool for degenerate strings, called the subset wavelet tree (SubsetWT). A SubsetWT supports two basic operations on degenerate strings: subset-rank(i,c), which returns the number of subsets up to the i-th subset in the degenerate string that contain the symbol c; and subset-select(i,c), which returns the index in the degenerate string of the i-th subset that contains symbol c. These queries are analogs of rank and select queries that have been widely studied for ordinary strings. Via experiments in a real genomics application in which degenerate strings are fundamental, we show that subset wavelet trees are practical data structures, and in particular offer an attractive space-time tradeoff. Along the way we investigate data structures for supporting (normal) rank queries on base-4 and base-3 sequences, which may be of independent interest. Our C++ implementations of the data structures are available at https://github.com/jnalanko/SubsetWT.
Cite as
Jarno N. Alanko, Elena Biagi, Simon J. Puglisi, and Jaakko Vuohtoniemi. Subset Wavelet Trees. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{alanko_et_al:LIPIcs.SEA.2023.4,
author = {Alanko, Jarno N. and Biagi, Elena and Puglisi, Simon J. and Vuohtoniemi, Jaakko},
title = {{Subset Wavelet Trees}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {4:1--4:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.4},
URN = {urn:nbn:de:0030-drops-183549},
doi = {10.4230/LIPIcs.SEA.2023.4},
annote = {Keywords: degenerate strings, compressed data structures, succinct data structures, string processing, data structures, efficient algorithms}
}
Document
Engineering Shared-Memory Parallel Shuffling to Generate Random Permutations In-Place
Abstract
Shuffling is the process of placing elements into a random order such that any permutation occurs with equal probability. It is an important building block in virtually all scientific areas. We engineer, - to the best of our knowledge - for the first time, a practically fast, parallel shuffling algorithm with O(√n log n) parallel depth that requires only poly-logarithmic auxiliary memory (with high probability). In an empirical evaluation, we compare our implementations with a number of existing solutions on various computer architectures. Our algorithms consistently achieve the highest through-put on all machines. Further, we demonstrate that the runtime of our parallel algorithm is comparable to the time that other algorithms may take to acquire the memory from the operating system to copy the input.
Cite as
Manuel Penschuck. Engineering Shared-Memory Parallel Shuffling to Generate Random Permutations In-Place. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{penschuck:LIPIcs.SEA.2023.5,
author = {Penschuck, Manuel},
title = {{Engineering Shared-Memory Parallel Shuffling to Generate Random Permutations In-Place}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {5:1--5:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.5},
URN = {urn:nbn:de:0030-drops-183550},
doi = {10.4230/LIPIcs.SEA.2023.5},
annote = {Keywords: Shuffling, random permutation, parallelism, in-place, algorithm engineering, practical implementation}
}
Document
Proxying Betweenness Centrality Rankings in Temporal Networks
Abstract
Identifying influential nodes in a network is arguably one of the most important tasks in graph mining and network analysis. A large variety of centrality measures, all aiming at correctly quantifying a node’s importance in the network, have been formulated in the literature. One of the most cited ones is the betweenness centrality, formally introduced by Freeman (Sociometry, 1977). On the other hand, researchers have recently been very interested in capturing the dynamic nature of real-world networks by studying temporal graphs, rather than static ones. Clearly, centrality measures, including the betweenness centrality, have also been extended to temporal graphs. Buß et al. (KDD, 2020) gave algorithms to compute various notions of temporal betweenness centrality, including the perhaps most natural one - shortest temporal betweenness. Their algorithm computes centrality values of all nodes in time O(n³ T²), where n is the size of the network and T is the total number of time steps. For real-world networks, which easily contain tens of thousands of nodes, this complexity becomes prohibitive. Thus, it is reasonable to consider proxies for shortest temporal betweenness rankings that are more efficiently computed, and, therefore, allow for measuring the relative importance of nodes in very large temporal graphs. In this paper, we compare several such proxies on a diverse set of real-world networks. These proxies can be divided into global and local proxies. The considered global proxies include the exact algorithm for static betweenness (computed on the underlying graph), prefix foremost temporal betweenness of Buß et al., which is more efficiently computable than shortest temporal betweenness, and the recently introduced approximation approach of Santoro and Sarpe (WWW, 2022). As all of these global proxies are still expensive to compute on very large networks, we also turn to more efficiently computable local proxies. Here, we consider temporal versions of the ego-betweenness in the sense of Everett and Borgatti (Social Networks, 2005), standard degree notions, and a novel temporal degree notion termed the pass-through degree, that we introduce in this paper and which we consider to be one of our main contributions. We show that the pass-through degree, which measures the number of pairs of neighbors of a node that are temporally connected through it, can be computed in nearly linear time for all nodes in the network and we experimentally observe that it is surprisingly competitive as a proxy for shortest temporal betweenness.
Cite as
Ruben Becker, Pierluigi Crescenzi, Antonio Cruciani, and Bojana Kodric. Proxying Betweenness Centrality Rankings in Temporal Networks. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{becker_et_al:LIPIcs.SEA.2023.6,
author = {Becker, Ruben and Crescenzi, Pierluigi and Cruciani, Antonio and Kodric, Bojana},
title = {{Proxying Betweenness Centrality Rankings in Temporal Networks}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {6:1--6:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.6},
URN = {urn:nbn:de:0030-drops-183568},
doi = {10.4230/LIPIcs.SEA.2023.6},
annote = {Keywords: node centrality, betweenness, temporal graphs, graph mining}
}
Document
Simple Runs-Bounded FM-Index Designs Are Fast
Abstract
Given a string X of length n on alphabet σ, the FM-index data structure allows counting all occurrences of a pattern P of length m in O(m) time via an algorithm called backward search. An important difficulty when searching with an FM-index is to support queries on L, the Burrows-Wheeler transform of X, while L is in compressed form. This problem has been the subject of intense research for 25 years now. Run-length encoding of L is an effective way to reduce index size, in particular when the data being indexed is highly-repetitive, which is the case in many types of modern data, including those arising from versioned document collections and in pangenomics. This paper takes a back-to-basics look at supporting backward search in FM-indexes, exploring and engineering two simple designs. The first divides the BWT string into blocks containing b symbols each and then run-length compresses each block separately, possibly introducing new runs (compared to applying run-length encoding once, to the whole string). Each block stores counts of each symbol that occurs before the block. This method supports the operation rank_c(L, i) (i.e., count the number of times c occurs in the prefix L[1..i]) by first determining the block i/b in which i falls and scanning the block to the appropriate position counting occurrences of c along the way. This partial answer to rank_c(L, i) is then added to the stored count of c symbols before the block to determine the final answer. Our second design has a similar structure, but instead divides the run-length-encoded version of L into blocks containing an equal number of runs. The trick then is to determine the block in which a query falls, which is achieved via a predecessor query over the block starting positions. We show via extensive experiments on a wide range of repetitive text collections that these FM-indexes are not only easy to implement, but also fast and space efficient in practice.
Cite as
Diego Díaz-Domínguez, Saska Dönges, Simon J. Puglisi, and Leena Salmela. Simple Runs-Bounded FM-Index Designs Are Fast. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{diazdominguez_et_al:LIPIcs.SEA.2023.7,
author = {D{\'\i}az-Dom{\'\i}nguez, Diego and D\"{o}nges, Saska and Puglisi, Simon J. and Salmela, Leena},
title = {{Simple Runs-Bounded FM-Index Designs Are Fast}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {7:1--7:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.7},
URN = {urn:nbn:de:0030-drops-183579},
doi = {10.4230/LIPIcs.SEA.2023.7},
annote = {Keywords: data structures, efficient algorithms}
}
Document
Noisy Sorting Without Searching: Data Oblivious Sorting with Comparison Errors
Abstract
We provide and study several algorithms for sorting an array of n comparable distinct elements subject to probabilistic comparison errors. In this model, the comparison of two elements returns the wrong answer according to a fixed probability, p_e < 1/2, and otherwise returns the correct answer. The dislocation of an element is the distance between its position in a given (current or output) array and its position in a sorted array. There are various algorithms that can be utilized for sorting or near-sorting elements subject to probabilistic comparison errors, but these algorithms are not data oblivious because they all make heavy use of noisy binary searching. In this paper, we provide new methods for sorting with comparison errors that are data oblivious while avoiding the use of noisy binary search methods. In addition, we experimentally compare our algorithms and other sorting algorithms.
Cite as
Ramtin Afshar, Michael Dillencourt, Michael T. Goodrich, and Evrim Ozel. Noisy Sorting Without Searching: Data Oblivious Sorting with Comparison Errors. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{afshar_et_al:LIPIcs.SEA.2023.8,
author = {Afshar, Ramtin and Dillencourt, Michael and Goodrich, Michael T. and Ozel, Evrim},
title = {{Noisy Sorting Without Searching: Data Oblivious Sorting with Comparison Errors}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {8:1--8:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.8},
URN = {urn:nbn:de:0030-drops-183585},
doi = {10.4230/LIPIcs.SEA.2023.8},
annote = {Keywords: sorting, algorithms, randomization, experimentation}
}
Document
Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem
Abstract
Optimizing over the efficient set of a discrete multi-objective problem is a challenging issue. The main reason is that, unlike when optimizing over the feasible set, the efficient set is implicitly characterized. Therefore, methods designed for this purpose iteratively generate efficient solutions by solving appropriate single-objective problems. However, the number of efficient solutions can be quite large and the problems to be solved can be difficult practically. Thus, the challenge is both to minimize the number of iterations and to reduce the difficulty of the problems to be solved at each iteration.
In this paper, a new enumeration scheme is proposed. By introducing some constraints and optimizing over projections of the search region, potentially large parts of the search space can be discarded, drastically reducing the number of iterations. Moreover, the single-objective programs to be solved can be guaranteed to be feasible, and a starting solution can be provided allowing warm start resolutions. This results in a fast algorithm that is simple to implement.
Experimental computations on two standard multi-objective instance families show that our approach seems to perform significantly faster than the state of the art algorithm.
Cite as
Satya Tamby and Daniel Vanderpooten. Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{tamby_et_al:LIPIcs.SEA.2023.9,
author = {Tamby, Satya and Vanderpooten, Daniel},
title = {{Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {9:1--9:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.9},
URN = {urn:nbn:de:0030-drops-183599},
doi = {10.4230/LIPIcs.SEA.2023.9},
annote = {Keywords: discrete optimization, multi-objective optimization, non-dominated set, efficient set}
}
Document
Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover
Abstract
In the Directed Feedback Vertex Set (DFVS) problem, one is given a directed graph G = (V,E) and wants to find a minimum cardinality set S ⊆ V such that G-S is acyclic. DFVS is a fundamental problem in computer science and finds applications in areas such as deadlock detection. The problem was the subject of the 2022 PACE coding challenge. We develop a novel exact algorithm for the problem that is tailored to perform well on instances that are mostly bi-directed. For such instances, we adapt techniques from the well-researched vertex cover problem. Our core idea is an iterative reduction to vertex cover. To this end, we also develop a new reduction rule that reduces the number of not bi-directed edges. With the resulting algorithm, we were able to win third place in the exact track of the PACE challenge. We perform computational experiments and compare the running time to other exact algorithms, in particular to the winning algorithm in PACE. Our experiments show that we outpace the other algorithms on instances that have a low density of uni-directed edges.
Cite as
Sebastian Angrick, Ben Bals, Katrin Casel, Sarel Cohen, Tobias Friedrich, Niko Hastrich, Theresa Hradilak, Davis Issac, Otto Kißig, Jonas Schmidt, and Leo Wendt. Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{angrick_et_al:LIPIcs.SEA.2023.10,
author = {Angrick, Sebastian and Bals, Ben and Casel, Katrin and Cohen, Sarel and Friedrich, Tobias and Hastrich, Niko and Hradilak, Theresa and Issac, Davis and Ki{\ss}ig, Otto and Schmidt, Jonas and Wendt, Leo},
title = {{Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {10:1--10:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.10},
URN = {urn:nbn:de:0030-drops-183602},
doi = {10.4230/LIPIcs.SEA.2023.10},
annote = {Keywords: directed feedback vertex set, vertex cover, reduction rules}
}
Document
CompDP: A Framework for Simultaneous Subgraph Counting Under Connectivity Constraints
Abstract
The subgraph counting problem computes the number of subgraphs of a given graph that satisfy some constraints. Among various constraints imposed on a graph, those regarding the connectivity of vertices, such as "these two vertices must be connected," have great importance since they are indispensable for determining various graph substructures, e.g., paths, Steiner trees, and rooted spanning forests. In this view, the subgraph counting problem under connectivity constraints is also important because counting such substructures often corresponds to measuring the importance of a vertex in network infrastructures. However, we must solve the subgraph counting problems multiple times to compute such an importance measure for every vertex. Conventionally, they are solved separately by constructing decision diagrams such as BDD and ZDD for each problem. However, even solving a single subgraph counting is a computationally hard task, preventing us from solving it multiple times in a reasonable time. In this paper, we propose a dynamic programming framework that simultaneously counts subgraphs for every vertex by focusing on similar connectivity constraints. Experimental results show that the proposed method solved multiple subgraph counting problems about 10-20 times faster than the existing approach for many problem settings.
Cite as
Kengo Nakamura, Masaaki Nishino, Norihito Yasuda, and Shin-ichi Minato. CompDP: A Framework for Simultaneous Subgraph Counting Under Connectivity Constraints. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{nakamura_et_al:LIPIcs.SEA.2023.11,
author = {Nakamura, Kengo and Nishino, Masaaki and Yasuda, Norihito and Minato, Shin-ichi},
title = {{CompDP: A Framework for Simultaneous Subgraph Counting Under Connectivity Constraints}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {11:1--11:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.11},
URN = {urn:nbn:de:0030-drops-183613},
doi = {10.4230/LIPIcs.SEA.2023.11},
annote = {Keywords: Subgraph counting, Connectivity, Zero-suppressed Binary Decision Diagram}
}
Document
Multilinear Formulations for Computing a Nash Equilibrium of Multi-Player Games
Abstract
We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player noncooperative games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended for large games. Hence, the multilinear feasibility program is an alternative method to find a Nash equilibrium in multi-player games, and outperforms many common algorithms. The mixed-integer formulations are generalisations of known mixed-integer programs for two-player games, however unlike two-player games, these mixed-integer programs do not give better performance than existing algorithms.
Cite as
Miriam Fischer and Akshay Gupte. Multilinear Formulations for Computing a Nash Equilibrium of Multi-Player Games. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{fischer_et_al:LIPIcs.SEA.2023.12,
author = {Fischer, Miriam and Gupte, Akshay},
title = {{Multilinear Formulations for Computing a Nash Equilibrium of Multi-Player Games}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {12:1--12:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.12},
URN = {urn:nbn:de:0030-drops-183620},
doi = {10.4230/LIPIcs.SEA.2023.12},
annote = {Keywords: Noncooperative n-person games, Nash equilibrium, Multilinear functions, Nonconvex problems, Mixed-integer optimization}
}
Document
Integer Programming Formulations and Cutting Plane Algorithms for the Maximum Selective Tree Problem
Abstract
This paper considers the Maximum Selective Tree Problem (MSelTP) as a generalization of the Maximum Induced Tree problem. Given an undirected graph with a partition of its vertex set into clusters, MSelTP aims to choose the maximum number of vertices such that at most one vertex per cluster is selected and the graph induced by the selected vertices is a tree. To the best of our knowledge, MSelTP has not been studied before although several related optimization problems have been investigated in the literature. We propose two mixed integer programming formulations for MSelTP; one based on connectivity constraints, the other based on cycle elimination constraints. In addition, we develop two exact cutting plane procedures to solve the problem to optimality. On graphs with up to 25 clusters, up to 250 vertices, and varying densities, we conduct computational experiments to compare the results of two solution procedures with solving a compact integer programming formulation of MSelTP. Our experiments indicate that the algorithm CPAXnY outperforms the other procedures overall except for graphs with low density and large cluster size, and that the algorithm CPAX yields better results in terms of the average time of instances optimally solved and the overall average time.
Cite as
Ömer Burak Onar, Tınaz Ekim, and Z. Caner Taşkın. Integer Programming Formulations and Cutting Plane Algorithms for the Maximum Selective Tree Problem. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{onar_et_al:LIPIcs.SEA.2023.13,
author = {Onar, \"{O}mer Burak and Ekim, T{\i}naz and Ta\c{s}k{\i}n, Z. Caner},
title = {{Integer Programming Formulations and Cutting Plane Algorithms for the Maximum Selective Tree Problem}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {13:1--13:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.13},
URN = {urn:nbn:de:0030-drops-183634},
doi = {10.4230/LIPIcs.SEA.2023.13},
annote = {Keywords: maximum induced tree, selective tree, cutting plane, separation algorithm, mixed integer programming}
}
Document
A Graph-Theoretic Formulation of Exploratory Blockmodeling
Abstract
We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G' with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G' directly give the blocks and block interactions of the computed blockmodel.
We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ≥ 4.
Cite as
Alexander Bille, Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. A Graph-Theoretic Formulation of Exploratory Blockmodeling. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bille_et_al:LIPIcs.SEA.2023.14,
author = {Bille, Alexander and Gr\"{u}ttemeier, Niels and Komusiewicz, Christian and Morawietz, Nils},
title = {{A Graph-Theoretic Formulation of Exploratory Blockmodeling}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {14:1--14:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.14},
URN = {urn:nbn:de:0030-drops-183648},
doi = {10.4230/LIPIcs.SEA.2023.14},
annote = {Keywords: Clustering, Exact Algorithms, ILP-Formulation, Branch-and-Bound, Social Networks}
}
Document
FREIGHT: Fast Streaming Hypergraph Partitioning
Abstract
Partitioning the vertices of a (hyper)graph into k roughly balanced blocks such that few (hyper)edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge (hyper)graphs using low computational resources are streaming algorithms. In this work, we propose FREIGHT: a Fast stREamInG Hypergraph parTitioning algorithm which is an adaptation of the widely-known graph-based algorithm Fennel. By using an efficient data structure, we make the overall running of FREIGHT linearly dependent on the pin-count of the hypergraph and the memory consumption linearly dependent on the numbers of nets and blocks. The results of our extensive experimentation showcase the promising performance of FREIGHT as a highly efficient and effective solution for streaming hypergraph partitioning. Our algorithm demonstrates competitive running time with the Hashing algorithm, with a difference of a maximum factor of four observed on three fourths of the instances. Significantly, our findings highlight the superiority of FREIGHT over all existing (buffered) streaming algorithms and even the in-memory algorithm HYPE, with respect to both cut-net and connectivity measures. This indicates that our proposed algorithm is a promising hypergraph partitioning tool to tackle the challenge posed by large-scale and dynamic data processing.
Cite as
Kamal Eyubov, Marcelo Fonseca Faraj, and Christian Schulz. FREIGHT: Fast Streaming Hypergraph Partitioning. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{eyubov_et_al:LIPIcs.SEA.2023.15,
author = {Eyubov, Kamal and Fonseca Faraj, Marcelo and Schulz, Christian},
title = {{FREIGHT: Fast Streaming Hypergraph Partitioning}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {15:1--15:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.15},
URN = {urn:nbn:de:0030-drops-183657},
doi = {10.4230/LIPIcs.SEA.2023.15},
annote = {Keywords: Hypergraph partitioning, graph partitioning, edge partitioning, streaming}
}
Document
Arc-Flags Meet Trip-Based Public Transit Routing
Abstract
We present Arc-Flag TB, a journey planning algorithm for public transit networks which combines Trip-Based Public Transit Routing (TB) with the Arc-Flags speedup technique. Compared to previous attempts to apply Arc-Flags to public transit networks, which saw limited success, our approach uses stronger pruning rules to reduce the search space. Our experiments show that Arc-Flag TB achieves a speedup of up to two orders of magnitude over TB, offering query times of less than a millisecond even on large countrywide networks. Compared to the state-of-the-art speedup technique Trip-Based Public Transit Routing Using Condensed Search Trees (TB-CST), our algorithm achieves similar query times but requires significantly less additional memory. Other state-of-the-art algorithms which achieve even faster query times, e.g., Public Transit Labeling, require enormous memory usage. In contrast, Arc-Flag TB offers a tradeoff between query performance and memory usage due to the fact that the number of regions in the network partition required by our algorithm is a configurable parameter. We also identify a previously undiscovered issue in the transfer precomputation of TB, which causes both TB-CST and Arc-Flag TB to answer some queries incorrectly. We provide discussion on how to resolve this issue in the future. Currently, Arc-Flag TB answers 1-6% of queries incorrectly, compared to over 20% for TB-CST on some networks.
Cite as
Ernestine Großmann, Jonas Sauer, Christian Schulz, and Patrick Steil. Arc-Flags Meet Trip-Based Public Transit Routing. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{gromann_et_al:LIPIcs.SEA.2023.16,
author = {Gro{\ss}mann, Ernestine and Sauer, Jonas and Schulz, Christian and Steil, Patrick},
title = {{Arc-Flags Meet Trip-Based Public Transit Routing}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {16:1--16:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.16},
URN = {urn:nbn:de:0030-drops-183664},
doi = {10.4230/LIPIcs.SEA.2023.16},
annote = {Keywords: Public transit routing, graph algorithms, algorithm engineering}
}
Document
Greedy Heuristics for Judicious Hypergraph Partitioning
Abstract
We investigate the efficacy of greedy heuristics for the judicious hypergraph partitioning problem. In contrast to balanced partitioning problems, the goal of judicious hypergraph partitioning is to minimize the maximum load over all blocks of the partition. We devise strategies for initial partitioning and FM-style post-processing. In combination with a multilevel scheme, they beat the previous state-of-the-art solver - based on greedy set covers - in both running time (two to four orders of magnitude) and solution quality (18% to 45%). A major challenge that makes local greedy approaches difficult to use for this problem is the high frequency of zero-gain moves, for which we present and evaluate counteracting mechanisms.
Cite as
Noah Wahl and Lars Gottesbüren. Greedy Heuristics for Judicious Hypergraph Partitioning. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{wahl_et_al:LIPIcs.SEA.2023.17,
author = {Wahl, Noah and Gottesb\"{u}ren, Lars},
title = {{Greedy Heuristics for Judicious Hypergraph Partitioning}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {17:1--17:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.17},
URN = {urn:nbn:de:0030-drops-183674},
doi = {10.4230/LIPIcs.SEA.2023.17},
annote = {Keywords: hypergraph partitioning, local search algorithms, load balancing, local search}
}
Document
Hierarchical Relative Lempel-Ziv Compression
Abstract
Relative Lempel-Ziv (RLZ) parsing is a dictionary compression method in which a string S is compressed relative to a second string R (called the reference) by parsing S into a sequence of substrings that occur in R. RLZ is particularly effective at compressing sets of strings that have a high degree of similarity to the reference string, such as a set of genomes of individuals from the same species. With the now cheap cost of DNA sequencing, such datasets have become extremely abundant and are rapidly growing. In this paper, instead of using a single reference string for the entire collection, we investigate the use of different reference strings for subsets of the collection, with the aim of improving compression. In particular, we propose a new compression scheme hierarchical relative Lempel-Ziv (HRLZ) which form a rooted tree (or hierarchy) on the strings and then compress each string using RLZ with parent as reference, storing only the root of the tree in plain text. To decompress, we traverse the tree in BFS order starting at the root, decompressing children with respect to their parent. We show that this approach leads to a twofold improvement in compression on bacterial genome datasets, with negligible effect on decompression time compared to the standard single reference approach. We show that an effective hierarchy for a given set of strings can be constructed by computing the optimal arborescence of a completed weighted digraph of the strings, with weights as the number of phrases in the RLZ parsing of the source and destination vertices. We further show that instead of computing the complete graph, a sparse graph derived using locality-sensitive hashing can significantly reduce the cost of computing a good hierarchy, without adversely effecting compression performance.
Cite as
Philip Bille, Inge Li Gørtz, Simon J. Puglisi, and Simon R. Tarnow. Hierarchical Relative Lempel-Ziv Compression. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{bille_et_al:LIPIcs.SEA.2023.18,
author = {Bille, Philip and G{\o}rtz, Inge Li and Puglisi, Simon J. and Tarnow, Simon R.},
title = {{Hierarchical Relative Lempel-Ziv Compression}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.18},
URN = {urn:nbn:de:0030-drops-183680},
doi = {10.4230/LIPIcs.SEA.2023.18},
annote = {Keywords: Relative compression, Lempel-Ziv compression, RLZ, LZ77, string collections, compressed representation, data structures, efficient algorithms}
}
Document
Exact and Approximate Range Mode Query Data Structures in Practice
Abstract
We conduct an experimental study on the range mode problem. In the exact version of the problem, we preprocess an array A, such that given a query range [a, b], the most frequent element in A[a, b] can be found efficiently. For this problem, our most important finding is that the strategy of using succinct data structures to encode more precomputed information not only helped Chan et al. (Linear-space data structures for range mode query in arrays, Theory of Computing Systems, 2013) improve previous results in theory but also helps us achieve the best time/space tradeoff in practice; we even go a step further to replace more components in their solution with succinct data structures and improve the performance further.
In the approximate version of this problem, a (1+ε)-approximate range mode query looks for an element whose occurrences in A[a,b] is at least F_{a,b}/(1+ε), where F_{a,b} is the frequency of the mode in A[a,b]. We implement all previous solutions to this problems and find that, even when ε = 1/2, the average approximation ratio of these solutions is close to 1 in practice, and they provide much faster query time than the best exact solution. These solutions achieve different useful time-space tradeoffs, and among them, El-Zein et al. (On Approximate Range Mode and Range Selection, 30th International Symposium on Algorithms and Computation, 2019) provide us with one solution whose space usage is only 35.6% to 93.8% of the cost of storing the input array of 32-bit integers (in most cases, the space cost is closer to the lower end, and the average space cost is 20.2 bits per symbol among all datasets). Its non-succinct version also stands out with query support at least several times faster than other O(n/ε)-word structures while using only slightly more space in practice.
Cite as
Meng He and Zhen Liu. Exact and Approximate Range Mode Query Data Structures in Practice. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{he_et_al:LIPIcs.SEA.2023.19,
author = {He, Meng and Liu, Zhen},
title = {{Exact and Approximate Range Mode Query Data Structures in Practice}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {19:1--19:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.19},
URN = {urn:nbn:de:0030-drops-183693},
doi = {10.4230/LIPIcs.SEA.2023.19},
annote = {Keywords: range mode query, exact range mode query, approximate range mode query}
}
Document
Efficient Yao Graph Construction
Abstract
Yao graphs are geometric spanners that connect each point of a given point set to its nearest neighbor in each of k cones drawn around it. Yao graphs were introduced to construct minimum spanning trees in d dimensional spaces. Moreover, they are used for instance in topology control in wireless networks. An optimal 𝒪(n log n)-time algorithm to construct Yao graphs for a given point set has been proposed in the literature but - to the best of our knowledge - never been implemented. Instead, algorithms with a quadratic complexity are used in popular packages to construct these graphs. In this paper we present the first implementation of the optimal Yao graph algorithm. We engineer the data structures required to achieve the 𝒪(n log n) time bound and detail algorithmic adaptations necessary to take the original algorithm from theory to practice. We propose a priority queue data structure that separates static and dynamic events and might be of independent interest for other sweepline algorithms. Additionally, we propose a new Yao graph algorithm based on a uniform grid data structure that performs well for medium-sized inputs. We evaluate our implementations on a wide variety of synthetic and real-world datasets and show that our implementation outperforms current publicly available implementations by at least an order of magnitude.
Cite as
Daniel Funke and Peter Sanders. Efficient Yao Graph Construction. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{funke_et_al:LIPIcs.SEA.2023.20,
author = {Funke, Daniel and Sanders, Peter},
title = {{Efficient Yao Graph Construction}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {20:1--20:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.20},
URN = {urn:nbn:de:0030-drops-183706},
doi = {10.4230/LIPIcs.SEA.2023.20},
annote = {Keywords: computational geometry, geometric spanners, Yao graphs, sweepline algorithms, optimal algorithms}
}
Document
Maximum Coverage in Sublinear Space, Faster
Abstract
Given a collection of m sets from a universe 𝒰, the Maximum Set Coverage problem consists of finding k sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial time algorithm up to a factor 1-1/e. However, this algorithm does not scale well with the input size.
In a streaming context, practical high-quality solutions are found, but with space complexity that scales linearly with respect to the size of the universe n = |𝒰|. However, one randomized streaming algorithm has been shown to produce a 1-1/e-ε approximation of the optimal solution with a space complexity that scales only poly-logarithmically with respect to m and n. In order to achieve such a low space complexity, the authors used two techniques in their multi-pass approach:
- F₀-sketching, allows to determine with great accuracy the number of distinct elements in a set using less space than the set itself.
- Subsampling, consists of only solving the problem on a subspace of the universe. It is implemented using γ-independent hash functions.
This article focuses on the sublinear-space algorithm and highlights the time cost of these two techniques, especially subsampling. We present optimizations that significantly reduce the time complexity of the algorithm. Firstly, we give some optimizations that do not alter the space complexity, number of passes and approximation quality of the original algorithm. In particular, we reanalyze the error bounds to show that the original independence factor of Ω(ε^{-2} k log m) can be fine-tuned to Ω(k log m); we also show how F₀-sketching can be removed. Secondly, we derive a new lower bound for the probability of producing a 1-1/e-ε approximation using only pairwise independence: 1- (4/(c k log m)) compared to 1-(2e/(m^{ck/6})) with Ω(k log m)-independence.
Although the theoretical guarantees are weaker, suggesting the approximation quality would suffer, for large streams, our algorithms perform well in practice. Finally, our experimental results show that even a pairwise-independent hash-function sampler does not produce worse solution than the original algorithm, while running significantly faster by several orders of magnitude.
Cite as
Stephen Jaud, Anthony Wirth, and Farhana Choudhury. Maximum Coverage in Sublinear Space, Faster. In 21st International Symposium on Experimental Algorithms (SEA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 265, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{jaud_et_al:LIPIcs.SEA.2023.21,
author = {Jaud, Stephen and Wirth, Anthony and Choudhury, Farhana},
title = {{Maximum Coverage in Sublinear Space, Faster}},
booktitle = {21st International Symposium on Experimental Algorithms (SEA 2023)},
pages = {21:1--21:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-279-2},
ISSN = {1868-8969},
year = {2023},
volume = {265},
editor = {Georgiadis, Loukas},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2023.21},
URN = {urn:nbn:de:0030-drops-183715},
doi = {10.4230/LIPIcs.SEA.2023.21},
annote = {Keywords: streaming algorithms, subsampling, maximum set cover, k-wise independent hash functions}
}