Pub Date : 2020-01-29DOI: 10.4230/LIPIcs.SEA.2020.20
Frances Cooper, D. Manlove
We study the problem of finding "fair" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). For an instance $I$ of SMI there may be many stable matchings, providing significantly different outcomes for the sets of men and women. We introduce two new notions of fairness in SMI. Firstly, a regret-equal stable matching minimises the difference in ranks of a worst-off man and a worst-off woman, among all stable matchings. Secondly, a min-regret sum stable matching minimises the sum of ranks of a worst-off man and a worst-off woman, among all stable matchings. We present two new efficient algorithms to find stable matchings of these types. Firstly, the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in $O(d_0 nm)$ time, where $d_0$ is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, $n$ is the number of men or women, and $m$ is the total length of all preference lists. Secondly, the Min-Regret Sum Algorithm finds a min-regret sum stable matching in $O(d_s m)$ time, where $d_s$ is the difference in the ranks between a worst-off man in each of the woman-optimal and man-optimal stable matchings. Experiments to compare several types of fair optimal stable matchings were conducted and show that the Regret-Equal Degree Iteration Algorithm produces matchings that are competitive with respect to other fairness objectives. On the other hand, existing types of "fair" stable matchings did not provide as close an approximation to regret-equal stable matchings.
{"title":"Algorithms for new types of fair stable matchings","authors":"Frances Cooper, D. Manlove","doi":"10.4230/LIPIcs.SEA.2020.20","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.20","url":null,"abstract":"We study the problem of finding \"fair\" stable matchings in the Stable Marriage problem with Incomplete lists (SMI). For an instance $I$ of SMI there may be many stable matchings, providing significantly different outcomes for the sets of men and women. We introduce two new notions of fairness in SMI. Firstly, a regret-equal stable matching minimises the difference in ranks of a worst-off man and a worst-off woman, among all stable matchings. Secondly, a min-regret sum stable matching minimises the sum of ranks of a worst-off man and a worst-off woman, among all stable matchings. We present two new efficient algorithms to find stable matchings of these types. Firstly, the Regret-Equal Degree Iteration Algorithm finds a regret-equal stable matching in $O(d_0 nm)$ time, where $d_0$ is the absolute difference in ranks between a worst-off man and a worst-off woman in the man-optimal stable matching, $n$ is the number of men or women, and $m$ is the total length of all preference lists. Secondly, the Min-Regret Sum Algorithm finds a min-regret sum stable matching in $O(d_s m)$ time, where $d_s$ is the difference in the ranks between a worst-off man in each of the woman-optimal and man-optimal stable matchings. Experiments to compare several types of fair optimal stable matchings were conducted and show that the Regret-Equal Degree Iteration Algorithm produces matchings that are competitive with respect to other fairness objectives. On the other hand, existing types of \"fair\" stable matchings did not provide as close an approximation to regret-equal stable matchings.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"5 1","pages":"20:1-20:13"},"PeriodicalIF":0.0,"publicationDate":"2020-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84661066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-28DOI: 10.4230/LIPIcs.SEA.2020.27
Meng He, Serikzhan Kazi
We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the $2d$ orthogonal range counting and reporting problems in planar point sets, to tree structured data. We propose practical realizations of the latest theoretical results on path queries. Our data structures, which use tree extraction, heavy-path decomposition and wavelet trees, are implemented in both succinct and pointer-based form. Our succinct data structures are further specialized to be plain or entropy-compressed. Through experiments on large sets, we show that succinct data structures for path queries may present a viable alternative to standard pointer-based realizations, in practical scenarios. Compared to na{"i}ve approaches that compute the answer by explicit traversal of the query path, our succinct data structures are several times faster in path median queries and perform comparably in path counting and path reporting queries, while being several times more space-efficient. Plain pointer-based realizations of our data structures, requiring a few times more space than the na{"i}ve ones, yield up to $100$-times speed-up over them.
{"title":"Path Query Data Structures in Practice","authors":"Meng He, Serikzhan Kazi","doi":"10.4230/LIPIcs.SEA.2020.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.27","url":null,"abstract":"We perform experimental studies on data structures that answer path median, path counting, and path reporting queries in weighted trees. These query problems generalize the well-known range median query problem in arrays, as well as the $2d$ orthogonal range counting and reporting problems in planar point sets, to tree structured data. We propose practical realizations of the latest theoretical results on path queries. Our data structures, which use tree extraction, heavy-path decomposition and wavelet trees, are implemented in both succinct and pointer-based form. Our succinct data structures are further specialized to be plain or entropy-compressed. Through experiments on large sets, we show that succinct data structures for path queries may present a viable alternative to standard pointer-based realizations, in practical scenarios. Compared to na{\"i}ve approaches that compute the answer by explicit traversal of the query path, our succinct data structures are several times faster in path median queries and perform comparably in path counting and path reporting queries, while being several times more space-efficient. Plain pointer-based realizations of our data structures, requiring a few times more space than the na{\"i}ve ones, yield up to $100$-times speed-up over them.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"65 1","pages":"27:1-27:16"},"PeriodicalIF":0.0,"publicationDate":"2020-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86837018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-20DOI: 10.4230/LIPIcs.SEA.2020.4
Marcelo Fonseca Faraj, Alexander van der Grinten, Henning Meyerhenke, J. Träff, Christian Schulz
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task is then to map the blocks of the partition onto the processors such that the overall communication cost is reduced. We present novel multilevel algorithms that integrate graph partitioning and process mapping. Important ingredients of our algorithm include fast label propagation, more localized local search, initial partitioning, as well as a compressed data structure to compute processor distances without storing a distance matrix. Experiments indicate that our algorithms speed up the overall mapping process and, due to the integrated multilevel approach, also find much better solutions in practice. For example, one configuration of our algorithm yields better solutions than the previous state-of-the-art in terms of mapping quality while being a factor 62 faster. Compared to the currently fastest iterated multilevel mapping algorithm Scotch, we obtain 16% better solutions while investing slightly more running time.
{"title":"High-Quality Hierarchical Process Mapping","authors":"Marcelo Fonseca Faraj, Alexander van der Grinten, Henning Meyerhenke, J. Träff, Christian Schulz","doi":"10.4230/LIPIcs.SEA.2020.4","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.4","url":null,"abstract":"Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task is then to map the blocks of the partition onto the processors such that the overall communication cost is reduced. We present novel multilevel algorithms that integrate graph partitioning and process mapping. Important ingredients of our algorithm include fast label propagation, more localized local search, initial partitioning, as well as a compressed data structure to compute processor distances without storing a distance matrix. Experiments indicate that our algorithms speed up the overall mapping process and, due to the integrated multilevel approach, also find much better solutions in practice. For example, one configuration of our algorithm yields better solutions than the previous state-of-the-art in terms of mapping quality while being a factor 62 faster. Compared to the currently fastest iterated multilevel mapping algorithm Scotch, we obtain 16% better solutions while investing slightly more running time.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"70 1","pages":"4:1-4:15"},"PeriodicalIF":0.0,"publicationDate":"2020-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73834135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.26
V. Buchhold, D. Delling, D. Schieferdecker, Michael Wegner
We study the problem of graph partitioning for evolving road networks. While the road network of the world is mostly stable, small updates happen on a relatively frequent basis, as can been observed with the OpenStreetMap project (http://www.openstreetmap.org). For various reasons, professional applications demand the graph partition to stay roughly the same over time, and that changes are limited to areas where graph updates occur. In this work, we define the problem, present algorithms to satisfy the stability needs, and evaluate our techniques on continental-sized road networks. Besides the stability gains, we show that, when the changes are low and local, running our novel techniques is an order of magnitude faster than running graph partitioning from scratch. 2012 ACM Subject Classification Mathematics of computing → Graph algorithms; Theory of computation → Dynamic graph algorithms
{"title":"Fast and Stable Repartitioning of Road Networks","authors":"V. Buchhold, D. Delling, D. Schieferdecker, Michael Wegner","doi":"10.4230/LIPIcs.SEA.2020.26","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.26","url":null,"abstract":"We study the problem of graph partitioning for evolving road networks. While the road network of the world is mostly stable, small updates happen on a relatively frequent basis, as can been observed with the OpenStreetMap project (http://www.openstreetmap.org). For various reasons, professional applications demand the graph partition to stay roughly the same over time, and that changes are limited to areas where graph updates occur. In this work, we define the problem, present algorithms to satisfy the stability needs, and evaluate our techniques on continental-sized road networks. Besides the stability gains, we show that, when the changes are low and local, running our novel techniques is an order of magnitude faster than running graph partitioning from scratch. 2012 ACM Subject Classification Mathematics of computing → Graph algorithms; Theory of computation → Dynamic graph algorithms","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"9 1","pages":"26:1-26:15"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74100944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.23
Elias Kuthe, S. Rahmann
The graph fused lasso optimization problem seeks, for a given input signal y = (yi) on nodes i ∈ V of a graph G = (V,E), a reconstructed signal x = (xi) that is both element-wise close to y in quadratic error and also has bounded total variation (sum of absolute differences across edges), thereby favoring regionally constant solutions. An important application is denoising of spatially correlated data, especially for medical images. Currently, fused lasso solvers for general graph input reduce the problem to an iteration over a series of “one-dimensional” problems (on paths or line graphs), which can be solved in linear time. Recently, a direct fused lasso algorithm for tree graphs has been presented, but no implementation of it appears to be available. We here present a simplified exact algorithm and additionally a fast approximation scheme for trees, together with engineered implementations for both. We empirically evaluate their performance on different kinds of trees with distinct degree distributions (simulated trees; spanning trees of road networks, grid graphs of images, social networks). The exact algorithm is very efficient on trees with low node degrees, which covers many naturally arising graphs, while the approximation scheme can perform better on trees with several higher-degree nodes when limiting the desired accuracy to values that are useful in practice. 2012 ACM Subject Classification Theory of computation → Mathematical optimization; Theory of computation → Dynamic programming; Mathematics of computing → Trees
{"title":"Engineering Fused Lasso Solvers on Trees","authors":"Elias Kuthe, S. Rahmann","doi":"10.4230/LIPIcs.SEA.2020.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.23","url":null,"abstract":"The graph fused lasso optimization problem seeks, for a given input signal y = (yi) on nodes i ∈ V of a graph G = (V,E), a reconstructed signal x = (xi) that is both element-wise close to y in quadratic error and also has bounded total variation (sum of absolute differences across edges), thereby favoring regionally constant solutions. An important application is denoising of spatially correlated data, especially for medical images. Currently, fused lasso solvers for general graph input reduce the problem to an iteration over a series of “one-dimensional” problems (on paths or line graphs), which can be solved in linear time. Recently, a direct fused lasso algorithm for tree graphs has been presented, but no implementation of it appears to be available. We here present a simplified exact algorithm and additionally a fast approximation scheme for trees, together with engineered implementations for both. We empirically evaluate their performance on different kinds of trees with distinct degree distributions (simulated trees; spanning trees of road networks, grid graphs of images, social networks). The exact algorithm is very efficient on trees with low node degrees, which covers many naturally arising graphs, while the approximation scheme can perform better on trees with several higher-degree nodes when limiting the desired accuracy to values that are useful in practice. 2012 ACM Subject Classification Theory of computation → Mathematical optimization; Theory of computation → Dynamic programming; Mathematics of computing → Trees","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"47 1","pages":"23:1-23:14"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80736379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.8
D. Berend, Yochai Twitto
In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics – Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows. 2012 ACM Subject Classification Theory of computation→ Theory of randomized search heuristics; Theory of computation → Stochastic approximation
{"title":"Effect of Initial Assignment on Local Search Performance for Max Sat","authors":"D. Berend, Yochai Twitto","doi":"10.4230/LIPIcs.SEA.2020.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.8","url":null,"abstract":"In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics – Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows. 2012 ACM Subject Classification Theory of computation→ Theory of randomized search heuristics; Theory of computation → Stochastic approximation","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"172 1","pages":"8:1-8:14"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90230749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.1
Martin Aumüller
Similarity search problems in high-dimensional data arise in many areas of computer science such as data bases, image analysis, machine learning, and natural language processing. One of the most prominent problems is finding the k nearest neighbors of a data point q ∈ ℝ^d in a large set of data points S ⊂ ℝ^d, under same distance measure such as Euclidean distance. In contrast to lower dimensional settings, we do not know of worst-case efficient data structures for such search problems in high-dimensional data, i.e., data structures that are faster than a linear scan through the data set. However, there is a rich body of (often heuristic) approaches that solve nearest neighbor search problems much faster than such a scan on many real-world data sets. As a necessity, the term solve means that these approaches give approximate results that are close to the true k-nearest neighbors. In this talk, we survey recent approaches to nearest neighbor search and related problems. The talk consists of three parts: (1) What makes nearest neighbor search difficult? (2) How do current state-of-the-art algorithms work? (3) What are recent advances regarding similarity search on GPUs, in distributed settings, or in external memory?
{"title":"Algorithm Engineering for High-Dimensional Similarity Search Problems (Invited Talk)","authors":"Martin Aumüller","doi":"10.4230/LIPIcs.SEA.2020.1","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.1","url":null,"abstract":"Similarity search problems in high-dimensional data arise in many areas of computer science such as data bases, image analysis, machine learning, and natural language processing. One of the most prominent problems is finding the k nearest neighbors of a data point q ∈ ℝ^d in a large set of data points S ⊂ ℝ^d, under same distance measure such as Euclidean distance. In contrast to lower dimensional settings, we do not know of worst-case efficient data structures for such search problems in high-dimensional data, i.e., data structures that are faster than a linear scan through the data set. However, there is a rich body of (often heuristic) approaches that solve nearest neighbor search problems much faster than such a scan on many real-world data sets. As a necessity, the term solve means that these approaches give approximate results that are close to the true k-nearest neighbors. In this talk, we survey recent approaches to nearest neighbor search and related problems. The talk consists of three parts: (1) What makes nearest neighbor search difficult? (2) How do current state-of-the-art algorithms work? (3) What are recent advances regarding similarity search on GPUs, in distributed settings, or in external memory?","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"78 1","pages":"1:1-1:3"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82848492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.2
S. Edelkamp
We look at several proposals to engineer the set of fundamental searching and sorting algorithms. Aspects are improving locality of disk access and cache access, the efficiency tuning by reducing the number of branch mispredictions, and reducing at leading factors hidden in the Big-Oh notation. These studies in algorithm engineering, in turn, lead to exiting new algorithm designs. On the practical side, we will establish that efficient sorting and searching algorithms are in tight collaboration, as sorting is used for finding duplicates in disk-based search, and heap structures designed for efficient graph search can be exploited in classical and adaptive sorting. We indicate the effects of engineered sorting and searching for combined task and motion planning. 2012 ACM Subject Classification Theory of computation → Design and analysis of algorithms
{"title":"Algorithm Engineering for Sorting and Searching, and All That (Invited Talk)","authors":"S. Edelkamp","doi":"10.4230/LIPIcs.SEA.2020.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.2","url":null,"abstract":"We look at several proposals to engineer the set of fundamental searching and sorting algorithms. Aspects are improving locality of disk access and cache access, the efficiency tuning by reducing the number of branch mispredictions, and reducing at leading factors hidden in the Big-Oh notation. These studies in algorithm engineering, in turn, lead to exiting new algorithm designs. On the practical side, we will establish that efficient sorting and searching algorithms are in tight collaboration, as sorting is used for finding duplicates in disk-based search, and heap structures designed for efficient graph search can be exploited in classical and adaptive sorting. We indicate the effects of engineered sorting and searching for combined task and motion planning. 2012 ACM Subject Classification Theory of computation → Design and analysis of algorithms","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"7 1","pages":"2:1-2:3"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74953087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.24
R. Grossi, Andrea Marino, Shima Moghtasedi
The analysis of similar motions in a network provides useful information for different applications like route recommendation. We are interested in algorithms to efficiently retrieve trajectories that are similar to a given query trajectory. For this task many studies have focused on extracting the geometrical information of trajectories. In this paper we investigate the properties of trajectories moving along the paths of a network. We provide a similarity function by making use of both the temporal aspect of trajectories and the structure of the underlying network. We propose an approximation technique that offers the top-k similar trajectories with respect to a query trajectory in an efficient way with acceptable precision. We investigate our method over real-world networks, and our experimental results show the effectiveness of the proposed method.
{"title":"Finding Structurally and Temporally Similar Trajectories in Graphs","authors":"R. Grossi, Andrea Marino, Shima Moghtasedi","doi":"10.4230/LIPIcs.SEA.2020.24","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.24","url":null,"abstract":"The analysis of similar motions in a network provides useful information for different applications like route recommendation. We are interested in algorithms to efficiently retrieve trajectories that are similar to a given query trajectory. For this task many studies have focused on extracting the geometrical information of trajectories. In this paper we investigate the properties of trajectories moving along the paths of a network. We provide a similarity function by making use of both the temporal aspect of trajectories and the structure of the underlying network. We propose an approximation technique that offers the top-k similar trajectories with respect to a query trajectory in an efficient way with acceptable precision. We investigate our method over real-world networks, and our experimental results show the effectiveness of the proposed method.","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"73 1","pages":"24:1-24:13"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80023332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4230/LIPIcs.SEA.2020.3
N. Prezza
Text indexing is a classical algorithmic problem that has been studied for over four decades. The earliest optimal-time solution to the problem, the suffix tree [11], dates back to 1973 and requires up to two orders of magnitude more space than the text to be stored. In the year 2000, two breakthrough works [6, 3] showed that this space overhead is not necessary: both the index and the text can be stored in a space proportional to the text’s entropy. These contributions had an enormous impact in bioinformatics: nowadays, the two most widely-used DNA aligners employ compressed indexes [9, 8]. In recent years, it became apparent that entropy had reached its limits: modern datasets (for example, collections of thousands of human genomes) are extremely large but very repetitive and, by its very definition, entropy cannot compress repetitive texts [7]. To overcome this problem, a new generation of indexes based on dictionary compressors (for example, LZ77 and run-length BWT) emerged [7, 5, 1], together with generalizations of the indexing problem to labeled graphs [2, 10, 4]. This talk is a short and friendly survey of the landmarks of this fascinating path that took us from suffix trees to the most modern compressed indexes on labeled graphs. 2012 ACM Subject Classification Theory of computation → Data compression; Theory of computation → Sorting and searching; Theory of computation → Pattern matching
{"title":"Indexing Compressed Text: A Tale of Time and Space (Invited Talk)","authors":"N. Prezza","doi":"10.4230/LIPIcs.SEA.2020.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.SEA.2020.3","url":null,"abstract":"Text indexing is a classical algorithmic problem that has been studied for over four decades. The earliest optimal-time solution to the problem, the suffix tree [11], dates back to 1973 and requires up to two orders of magnitude more space than the text to be stored. In the year 2000, two breakthrough works [6, 3] showed that this space overhead is not necessary: both the index and the text can be stored in a space proportional to the text’s entropy. These contributions had an enormous impact in bioinformatics: nowadays, the two most widely-used DNA aligners employ compressed indexes [9, 8]. In recent years, it became apparent that entropy had reached its limits: modern datasets (for example, collections of thousands of human genomes) are extremely large but very repetitive and, by its very definition, entropy cannot compress repetitive texts [7]. To overcome this problem, a new generation of indexes based on dictionary compressors (for example, LZ77 and run-length BWT) emerged [7, 5, 1], together with generalizations of the indexing problem to labeled graphs [2, 10, 4]. This talk is a short and friendly survey of the landmarks of this fascinating path that took us from suffix trees to the most modern compressed indexes on labeled graphs. 2012 ACM Subject Classification Theory of computation → Data compression; Theory of computation → Sorting and searching; Theory of computation → Pattern matching","PeriodicalId":9448,"journal":{"name":"Bulletin of the Society of Sea Water Science, Japan","volume":"261 1","pages":"3:1-3:2"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76253699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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