Pub Date : 2023-01-01DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.22
Ilan Doron Arad, A. Kulik, H. Shachnai
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0 , 1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes , in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties
{"title":"An AFPTAS for Bin Packing with Partition Matroid via a New Method for LP Rounding","authors":"Ilan Doron Arad, A. Kulik, H. Shachnai","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.22","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.22","url":null,"abstract":"We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in [0 , 1], and a partition matroid over the items. The goal is to pack the items in a minimum number of unit-size bins, such that each bin forms an independent set in the matroid. This variant of classic Bin Packing has natural applications in secure storage on the Cloud, as well as in equitable scheduling and clustering with fairness constraints. Our main result is an asymptotic fully polynomial-time approximation scheme (AFPTAS) for Bin Packing with a partition matroid constraint. This scheme generalizes the known AFPTAS for Bin Packing with Cardinality Constraints and improves the existing asymptotic polynomial-time approximation scheme (APTAS) for Group Bin Packing, which are both special cases of Bin Packing with partition matroid. We derive the scheme via a new method for rounding a (fractional) solution for a configuration-LP. Our method uses this solution to obtain prototypes , in which items are interpreted as placeholders for other items, and applies fractional grouping to modify a fractional solution (prototype) into one having desired integrality properties","PeriodicalId":54319,"journal":{"name":"Spin","volume":"36 1","pages":"22:1-22:16"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80102531","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.2023.5
George Karakostas, Stavros G. Kolliopoulos
We study the classic weighted maximum throughput problem on unrelated machines. We give a (1 − 1 /e − ε )-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ -approximation algorithm for the single-machine problem to obtain an approximation factor of (1 − 1 /e ) ρ − ε for the corresponding unrelated-machines problem, for any ε > 0 . On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1 − 1 /e ) − ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine.
{"title":"Approximation Algorithms for Maximum Weighted Throughput on Unrelated Machines","authors":"George Karakostas, Stavros G. Kolliopoulos","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.5","url":null,"abstract":"We study the classic weighted maximum throughput problem on unrelated machines. We give a (1 − 1 /e − ε )-approximation algorithm for the preemptive case. To our knowledge this is the first ever approximation result for this problem. It is an immediate consequence of a polynomial-time reduction we design, that uses any ρ -approximation algorithm for the single-machine problem to obtain an approximation factor of (1 − 1 /e ) ρ − ε for the corresponding unrelated-machines problem, for any ε > 0 . On a single machine we present a PTAS for the non-preemptive version of the problem for the special case of a constant number of distinct due dates or distinct release dates. By our reduction this yields an approximation factor of (1 − 1 /e ) − ε for the non-preemptive problem on unrelated machines when there is a constant number of distinct due dates or release dates on each machine.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"148 1","pages":"5:1-5:17"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77783760","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.2023.31
R. Impagliazzo, Valentine Kabanets, Ilya Volkovich
We study close connections between Indistinguishability Obfuscation ( IO ) and the Minimum Circuit Size Problem ( MCSP ), and argue that efficient algorithms/construction for MCSP and IO create a synergy 1 . Some of our main results are: If there exists a perfect (imperfect) IO that is computationally secure against nonuniform polynomial-size circuits, then for all k ∈ N : NP
{"title":"Synergy Between Circuit Obfuscation and Circuit Minimization","authors":"R. Impagliazzo, Valentine Kabanets, Ilya Volkovich","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.31","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.31","url":null,"abstract":"We study close connections between Indistinguishability Obfuscation ( IO ) and the Minimum Circuit Size Problem ( MCSP ), and argue that efficient algorithms/construction for MCSP and IO create a synergy 1 . Some of our main results are: If there exists a perfect (imperfect) IO that is computationally secure against nonuniform polynomial-size circuits, then for all k ∈ N : NP","PeriodicalId":54319,"journal":{"name":"Spin","volume":"1 1","pages":"31:1-31:21"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83006265","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.2023.9
Matej Lieskovský, Jirí Sgall, A. Feldmann
Graph Burning models information spreading in a given graph as a process such that in each step one node is infected (informed) and also the infection spreads to all neighbors of previously infected nodes. Formally, given a graph G = ( V, E ), possibly with edge lengths, the burning number b ( G ) is the minimum number g such that there exist nodes v 0 , . . . , v g − 1 ∈ V satisfying the property that for each u ∈ V there exists i ∈ { 0 , . . . , g − 1 } so that the distance between u and v i is at most i . We present a randomized 2 . 314-approximation algorithm for computing the burning number of a general graph, even with arbitrary edge lengths. We complement this by an approximation lower bound of 2 for the case of equal length edges, and a lower bound of 4 / 3 for the case when edges are restricted to have length 1. This improves on the previous 3-approximation algorithm and an APX-hardness result.
{"title":"Approximation Algorithms and Lower Bounds for Graph Burning","authors":"Matej Lieskovský, Jirí Sgall, A. Feldmann","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.9","url":null,"abstract":"Graph Burning models information spreading in a given graph as a process such that in each step one node is infected (informed) and also the infection spreads to all neighbors of previously infected nodes. Formally, given a graph G = ( V, E ), possibly with edge lengths, the burning number b ( G ) is the minimum number g such that there exist nodes v 0 , . . . , v g − 1 ∈ V satisfying the property that for each u ∈ V there exists i ∈ { 0 , . . . , g − 1 } so that the distance between u and v i is at most i . We present a randomized 2 . 314-approximation algorithm for computing the burning number of a general graph, even with arbitrary edge lengths. We complement this by an approximation lower bound of 2 for the case of equal length edges, and a lower bound of 4 / 3 for the case when edges are restricted to have length 1. This improves on the previous 3-approximation algorithm and an APX-hardness result.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"17 1","pages":"9:1-9:17"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81954168","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.2023.2
Kamesh Munagala, Govind S. Sankar, Erin Taylor
We consider probabilistic embedding of metric spaces into ultra-metrics (or equivalently to a constant factor, into hierarchically separated trees) to minimize the expected distortion of any pairwise distance. Such embeddings have been widely used in network design and online algorithms. Our main result is a polynomial time algorithm that approximates the optimal distortion on any instance to within a constant factor. We achieve this via a novel LP formulation that reduces this problem to a probabilistic version of uniform metric labeling.
{"title":"Probabilistic Metric Embedding via Metric Labeling","authors":"Kamesh Munagala, Govind S. Sankar, Erin Taylor","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.2","url":null,"abstract":"We consider probabilistic embedding of metric spaces into ultra-metrics (or equivalently to a constant factor, into hierarchically separated trees) to minimize the expected distortion of any pairwise distance. Such embeddings have been widely used in network design and online algorithms. Our main result is a polynomial time algorithm that approximates the optimal distortion on any instance to within a constant factor. We achieve this via a novel LP formulation that reduces this problem to a probabilistic version of uniform metric labeling.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"27 1","pages":"2:1-2:10"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78146740","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_8
Benedikt Maderbacher, Stefan Schupp, E. Bartocci, Roderick Bloem, D. Ničković, Bettina Könighofer
{"title":"Provable Correct and Adaptive Simplex Architecture for Bounded-Liveness Properties","authors":"Benedikt Maderbacher, Stefan Schupp, E. Bartocci, Roderick Bloem, D. Ničković, Bettina Könighofer","doi":"10.1007/978-3-031-32157-3_8","DOIUrl":"https://doi.org/10.1007/978-3-031-32157-3_8","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":"54 1","pages":"141-160"},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76210646","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 : 2022-12-30DOI: 10.1142/s2010324723500042
Sunena Parida, Tapaswinee Jena, A. Sahu, R. Choudhary
{"title":"Study of structural, dielectric, electrical, and optical properties of the Sr3CuTi4O12 ceramics","authors":"Sunena Parida, Tapaswinee Jena, A. Sahu, R. Choudhary","doi":"10.1142/s2010324723500042","DOIUrl":"https://doi.org/10.1142/s2010324723500042","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45244086","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 : 2022-12-23DOI: 10.1142/s2010324723400015
A. A. Pasynkova, A. Timofeeva, V. A. Lukshina
{"title":"Functional properties of cobalt-based amorphous ribbons with different demagnetizing factor","authors":"A. A. Pasynkova, A. Timofeeva, V. A. Lukshina","doi":"10.1142/s2010324723400015","DOIUrl":"https://doi.org/10.1142/s2010324723400015","url":null,"abstract":"","PeriodicalId":54319,"journal":{"name":"Spin","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44943694","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：