455 research outputs found
Virtual Network Embedding Approximations: Leveraging Randomized Rounding
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems. In the VNEP, customers request resources in the form of Virtual Networks. An embedding of a virtual network on a shared physical infrastructure is the joint mapping of (virtual) nodes to physical servers together with the mapping of (virtual) edges onto paths in the physical network connecting the respective servers. This work initiates the study of approximation algorithms for the VNEP for general request graphs. Concretely, we study the offline setting with admission control: given multiple requests, the task is to embed the most profitable subset while not exceeding resource capacities. Our approximation is based on the randomized rounding of Linear Programming (LP) solutions. Interestingly, we uncover that the standard LP formulation for the VNEP exhibits an inherent structural deficit when considering general virtual network topologies: its solutions cannot be decomposed into valid embeddings. In turn, focusing on the class of cactus request graphs, we devise a novel LP formulation, whose solutions can be decomposed. Proving performance guarantees of our rounding scheme, we obtain the first approximation algorithm for the VNEP in the resource augmentation model. We propose different types of rounding heuristics and evaluate their performance in an extensive computational study. Our results indicate that good solutions can be achieved even without resource augmentations. Specifically, heuristical rounding achieves 77.2% of the baseline’s profit on average while respecting capacities.BMBF, 01IS12056, Software Campus GrantEC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNe
Structured Matrix Completion with Applications to Genomic Data Integration
Matrix completion has attracted significant recent attention in many fields
including statistics, applied mathematics and electrical engineering. Current
literature on matrix completion focuses primarily on independent sampling
models under which the individual observed entries are sampled independently.
Motivated by applications in genomic data integration, we propose a new
framework of structured matrix completion (SMC) to treat structured missingness
by design. Specifically, our proposed method aims at efficient matrix recovery
when a subset of the rows and columns of an approximately low-rank matrix are
observed. We provide theoretical justification for the proposed SMC method and
derive lower bound for the estimation errors, which together establish the
optimal rate of recovery over certain classes of approximately low-rank
matrices. Simulation studies show that the method performs well in finite
sample under a variety of configurations. The method is applied to integrate
several ovarian cancer genomic studies with different extent of genomic
measurements, which enables us to construct more accurate prediction rules for
ovarian cancer survival.Comment: Accepted for publication in Journal of the American Statistical
Associatio
The Boson peak in supercooled water
We perform extensive molecular dynamics simulations of the TIP4P/2005 model of water to investigate the origin of the Boson peak reported in experiments on supercooled water in nanoconfined pores and in hydration water around proteins. We find that the onset of the Boson peak in supercooled bulk water coincides with the crossover to a predominantly low-density-like liquid below the Widom line TW. The frequency and onset temperature of the Boson peak in our simulations of bulk water agree well with the results from experiments on nanoconfined water. Our results suggest that the Boson peak in water is not an exclusive effect of confinement. We further find that, similar to other glass-forming liquids, the vibrational modes corresponding to the Boson peak are spatially extended and are related to transverse phonons found in the parent crystal, here ice Ih.We thank S. V. Buldyrev and S. Sastry for helpful discussions. The simulations were in part performed using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the NSC and HPC2N centers. LGMP, KTW and DS were supported by the Swedish Research Council. KTW is also supported by the Icelandic Research Fund through the START programme. PK acknowledges the support of National Academies Keck Future Initiatives award. HES thanks NSF Grants No. CHE0911389, No. CHE0908218, and No. CHE-1213217. (Swedish Research Council; Icelandic Research Fund through the START programme; National Academies Keck Future Initiatives award; CHE0911389 - NSF; CHE0908218 - NSF; CHE-1213217 - NSF)Published versio
The Boson peak in supercooled water
We perform extensive molecular dynamics simulations of the TIP4P/2005 model
of water to investigate the origin of the Boson peak reported in experiments on
supercooled water in nanoconfined pores, and in hydration water around
proteins. We find that the onset of the Boson peak in supercooled bulk water
coincides with the crossover to a predominantly low-density-like liquid below
the Widom line . The frequency and onset temperature of the Boson peak in
our simulations of bulk water agree well with the results from experiments on
nanoconfined water. Our results suggest that the Boson peak in water is not an
exclusive effect of confinement. We further find that, similar to other
glass-forming liquids, the vibrational modes corresponding to the Boson peak
are spatially extended and are related to transverse phonons found in the
parent crystal, here ice Ih.Comment: 25 pages, 9 figure
Preferential attachment with information filtering - node degree probability distribution properties
A network growth mechanism based on a two-step preferential rule is
investigated as a model of network growth in which no global knowledge of the
network is required. In the first filtering step a subset of fixed size of
existing nodes is randomly chosen. In the second step the preferential rule of
attachment is applied to the chosen subset. The characteristics of thus formed
networks are explored using two approaches: computer simulations of network
growth and a theoretical description based on a master equation. The results of
the two approaches are in excellent agreement. Special emphasis is put on the
investigation of the node degree probability distribution. It is found that the
tail of the distribution has the exponential form given by .
Implications of the node degree distribution with such tail characteristics are
briefly discussed.Comment: v1:revtex, 7 pages, 8 figures. v2: version to appear in Physica
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