Submodular Norms with Applications To Online Facility Location and Stochastic Probing

IF 1.3 4区 物理与天体物理 Q4 PHYSICS, APPLIED Spin Pub Date : 2023-10-06 DOI:10.4230/LIPIcs.APPROX/RANDOM.2023.23
Kalen Patton, Matteo Russo, Sahil Singla
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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.
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子模规范在在线设备定位和随机探测中的应用
优化问题通常涉及向量规范,这导致了对开发算法的广泛研究,这些算法可以处理超出$\ell_p$规范的目标。我们的工作引入了子模模范数的概念,它是一种通用型范数,具有类似于子模集合函数的边际性质。我们证明了子模范数可以准确地表示或近似众所周知的范数类,如$\ell_p$范数、有序范数和对称范数。此外,我们还建立了子模规范可以应用于在线设施定位、随机探测和广义负载平衡等优化问题。这使我们能够开发具有对称范数的在线设施位置的对数竞争算法,证明具有对称范数的随机探测的对数自适应差距,并给出具有外部$\ell_1$范数和内部对称范数的广义负载平衡的替代多对数逼近算法。
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来源期刊
Spin
Spin Materials 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
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