Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.6
Morteza Monemizadeh
In the sublinear geometric model , we are provided with an oracle access to a point set P of n points in a bounded discrete space [∆] 2 , where ∆ = n O (1) is a polynomially bounded number in n . That is, we do not have direct access to the points, but we can make certain types of queries and there is an oracle that responds to our queries. The type of queries that we assume we can make in this paper, are range counting queries where ranges are axis-aligned rectangles (that are basic primitives in database [36, 11, 17], computational geometry [1, 2, 6, 5], and machine learning [35, 31, 29, 28]). The oracle then answers these queries by returning the number of points that are in queried ranges. Let Alg be an algorithm that (exactly or approximately) solves a problem P in the sublinear geometric model. The query complexity of Alg is measured in terms of the number of queries that Alg makes to solve P . In this paper, we study the complexity of the (uniform) Euclidean facility location problem in the sublinear geometric model. We develop a randomized sublinear algorithm that with high probability, (1 + ϵ )-approximates the cost of the Euclidean facility location problem of the point set P in the sublinear geometric model using ˜ O ( √ n ) range counting queries. We complement this result by showing that approximating the cost of the Euclidean facility location problem within o (log( n ))-factor in the sublinear geometric model using the sampling strategy that we propose for our sublinear algorithm needs ˜Ω( n 1 / 4 ) RangeCount queries. We leave it as an open problem whether such a polynomial lower bound on the number of RangeCount queries exists for any randomized sublinear algorithm that approximates the cost of the facility location problem within a constant factor.
{"title":"Facility Location in the Sublinear Geometric Model","authors":"Morteza Monemizadeh","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.6","url":null,"abstract":"In the sublinear geometric model , we are provided with an oracle access to a point set P of n points in a bounded discrete space [∆] 2 , where ∆ = n O (1) is a polynomially bounded number in n . That is, we do not have direct access to the points, but we can make certain types of queries and there is an oracle that responds to our queries. The type of queries that we assume we can make in this paper, are range counting queries where ranges are axis-aligned rectangles (that are basic primitives in database [36, 11, 17], computational geometry [1, 2, 6, 5], and machine learning [35, 31, 29, 28]). The oracle then answers these queries by returning the number of points that are in queried ranges. Let Alg be an algorithm that (exactly or approximately) solves a problem P in the sublinear geometric model. The query complexity of Alg is measured in terms of the number of queries that Alg makes to solve P . In this paper, we study the complexity of the (uniform) Euclidean facility location problem in the sublinear geometric model. We develop a randomized sublinear algorithm that with high probability, (1 + ϵ )-approximates the cost of the Euclidean facility location problem of the point set P in the sublinear geometric model using ˜ O ( √ n ) range counting queries. We complement this result by showing that approximating the cost of the Euclidean facility location problem within o (log( n ))-factor in the sublinear geometric model using the sampling strategy that we propose for our sublinear algorithm needs ˜Ω( n 1 / 4 ) RangeCount queries. We leave it as an open problem whether such a polynomial lower bound on the number of RangeCount queries exists for any randomized sublinear algorithm that approximates the cost of the facility location problem within a constant factor.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"75 1","pages":"6:1-6:24"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77551753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/978-3-031-32157-3_11
Anton Wijs, M. Osama
{"title":"GPUexplore 3.0: GPU Accelerated State Space Exploration for Concurrent Systems with Data","authors":"Anton Wijs, M. Osama","doi":"10.1007/978-3-031-32157-3_11","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_11","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"1 1","pages":"188-197"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82846418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/978-3-031-32157-3_10
E. Henriksen, A. M. Khorsid, Esben Nielsen, Theodor Risager, J. Srba, Adam M. Stück, Andreas S. Sørensen
{"title":"Potency-Based Heuristic Search with Randomness for Explicit Model Checking","authors":"E. Henriksen, A. M. Khorsid, Esben Nielsen, Theodor Risager, J. Srba, Adam M. Stück, Andreas S. Sørensen","doi":"10.1007/978-3-031-32157-3_10","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_10","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"1 1","pages":"180-187"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88307071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.16
Felix Höhne, R. V. Stee
In the discrete bamboo garden trimming problem we are given n bamboo that grow at rates v 1 , . . . , v n per day. Each day a robotic gardener cuts down one bamboo to height 0. The goal is to find a schedule that minimizes the height of the tallest bamboo that ever exists. We present a 10 / 7-approximation algorithm that is based on a reduction to the pinwheel problem. This is consistent with the approach of earlier algorithms, but some new techniques are used that lead to a better approximation ratio. We also consider the continuous version of the problem where the gardener travels in a metric space between plants and cuts down a plant each time he reaches one. We show that on the star graph the previously proposed algorithm Reduce-Fastest is a 6-approximation and the known Deadline-Driven Strategy is a (3 + 2 √ 2)-approximation. The Deadline-Driven Strategy is also a (9 + 2 √ 5)-approximation on star graphs with multiple plants on each branch.
{"title":"A 10/7-Approximation for Discrete Bamboo Garden Trimming and Continuous Trimming on Star Graphs","authors":"Felix Höhne, R. V. Stee","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.16","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.16","url":null,"abstract":"In the discrete bamboo garden trimming problem we are given n bamboo that grow at rates v 1 , . . . , v n per day. Each day a robotic gardener cuts down one bamboo to height 0. The goal is to find a schedule that minimizes the height of the tallest bamboo that ever exists. We present a 10 / 7-approximation algorithm that is based on a reduction to the pinwheel problem. This is consistent with the approach of earlier algorithms, but some new techniques are used that lead to a better approximation ratio. We also consider the continuous version of the problem where the gardener travels in a metric space between plants and cuts down a plant each time he reaches one. We show that on the star graph the previously proposed algorithm Reduce-Fastest is a 6-approximation and the known Deadline-Driven Strategy is a (3 + 2 √ 2)-approximation. The Deadline-Driven Strategy is also a (9 + 2 √ 5)-approximation on star graphs with multiple plants on each branch.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"82 1","pages":"16:1-16:19"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84219910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/978-3-031-32157-3_1
Lieuwe Vinkhuijzen, Thomas Grurl, S. Hillmich, Sebastiaan Brand, R. Wille, A. Laarman
{"title":"Efficient Implementation of LIMDDs for Quantum Circuit Simulation","authors":"Lieuwe Vinkhuijzen, Thomas Grurl, S. Hillmich, Sebastiaan Brand, R. Wille, A. Laarman","doi":"10.1007/978-3-031-32157-3_1","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_1","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"29 1","pages":"3-21"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76816557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.51
Yahli Hecht, Dor Minzer, S. Safra
A graph G = ( V, E ) is said to be ( k, δ ) almost colorable if there is a subset of vertices V ′ ⊆ V of size at least (1 − δ ) | V | such that the induced subgraph of G on V ′ is k -colorable. We prove that for all k , there exists δ > 0 such for all ε > 0, given a graph G it is NP-hard (under randomized reductions) to distinguish between:
{"title":"NP-Hardness of Almost Coloring Almost 3-Colorable Graphs","authors":"Yahli Hecht, Dor Minzer, S. Safra","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.51","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.51","url":null,"abstract":"A graph G = ( V, E ) is said to be ( k, δ ) almost colorable if there is a subset of vertices V ′ ⊆ V of size at least (1 − δ ) | V | such that the induced subgraph of G on V ′ is k -colorable. We prove that for all k , there exists δ > 0 such for all ε > 0, given a graph G it is NP-hard (under randomized reductions) to distinguish between:","PeriodicalId":54319,"journal":{"name":"Spin","volume":"25 2 1","pages":"51:1-51:12"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83522133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1007/978-3-031-32157-3_9
P. G. Jensen, K. Larsen, J. Srba, Nikolaj Jensen Ulrik
{"title":"Elimination of Detached Regions in Dependency Graph Verification","authors":"P. G. Jensen, K. Larsen, J. Srba, Nikolaj Jensen Ulrik","doi":"10.1007/978-3-031-32157-3_9","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_9","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"48 1","pages":"163-179"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87003096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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