{"title":"Submodular Norms with Applications To Online Facility Location and Stochastic Probing","authors":"Kalen Patton, Matteo Russo, Sahil Singla","doi":"10.4230/LIPIcs.APPROX/RANDOM.2023.23","DOIUrl":null,"url":null,"abstract":"Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile type of norms that possess marginal properties similar to submodular set functions. We show that submodular norms can accurately represent or approximate well-known classes of norms, such as $\\ell_p$ norms, ordered norms, and symmetric norms. Furthermore, we establish that submodular norms can be applied to optimization problems such as online facility location, stochastic probing, and generalized load balancing. This allows us to develop a logarithmic-competitive algorithm for online facility location with symmetric norms, to prove a logarithmic adaptivity gap for stochastic probing with symmetric norms, and to give an alternative poly-logarithmic approximation algorithm for generalized load balancing with outer $\\ell_1$ norm and inner symmetric norms.","PeriodicalId":54319,"journal":{"name":"Spin","volume":"5 1","pages":"23:1-23:22"},"PeriodicalIF":1.3000,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Spin","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.23","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
Optimization problems often involve vector norms, which has led to extensive research on developing algorithms that can handle objectives beyond the $\ell_p$ norms. Our work introduces the concept of submodular norms, which are a versatile type of norms that possess marginal properties similar to submodular set functions. We show that submodular norms can accurately represent or approximate well-known classes of norms, such as $\ell_p$ norms, ordered norms, and symmetric norms. Furthermore, we establish that submodular norms can be applied to optimization problems such as online facility location, stochastic probing, and generalized load balancing. This allows us to develop a logarithmic-competitive algorithm for online facility location with symmetric norms, to prove a logarithmic adaptivity gap for stochastic probing with symmetric norms, and to give an alternative poly-logarithmic approximation algorithm for generalized load balancing with outer $\ell_1$ norm and inner symmetric norms.
SpinMaterials Science-Electronic, Optical and Magnetic Materials
CiteScore
2.10
自引率
11.10%
发文量
34
期刊介绍:
Spin electronics encompasses a multidisciplinary research effort involving magnetism, semiconductor electronics, materials science, chemistry and biology. SPIN aims to provide a forum for the presentation of research and review articles of interest to all researchers in the field.
The scope of the journal includes (but is not necessarily limited to) the following topics:
*Materials:
-Metals
-Heusler compounds
-Complex oxides: antiferromagnetic, ferromagnetic
-Dilute magnetic semiconductors
-Dilute magnetic oxides
-High performance and emerging magnetic materials
*Semiconductor electronics
*Nanodevices:
-Fabrication
-Characterization
*Spin injection
*Spin transport
*Spin transfer torque
*Spin torque oscillators
*Electrical control of magnetic properties
*Organic spintronics
*Optical phenomena and optoelectronic spin manipulation
*Applications and devices:
-Novel memories and logic devices
-Lab-on-a-chip
-Others
*Fundamental and interdisciplinary studies:
-Spin in low dimensional system
-Spin in medical sciences
-Spin in other fields
-Computational materials discovery