5,615 research outputs found
Developing a Mathematical Model for Bobbin Lace
Bobbin lace is a fibre art form in which intricate and delicate patterns are
created by braiding together many threads. An overview of how bobbin lace is
made is presented and illustrated with a simple, traditional bookmark design.
Research on the topology of textiles and braid theory form a base for the
current work and is briefly summarized. We define a new mathematical model that
supports the enumeration and generation of bobbin lace patterns using an
intelligent combinatorial search. Results of this new approach are presented
and, by comparison to existing bobbin lace patterns, it is demonstrated that
this model reveals new patterns that have never been seen before. Finally, we
apply our new patterns to an original bookmark design and propose future areas
for exploration.Comment: 20 pages, 18 figures, intended audience includes Artists as well as
Computer Scientists and Mathematician
Spatially self-organized resilient networks by a distributed cooperative mechanism
The robustness of connectivity and the efficiency of paths are incompatible
in many real networks. We propose a self-organization mechanism for
incrementally generating onion-like networks with positive degree-degree
correlations whose robustness is nearly optimal. As a spatial extension of the
generation model based on cooperative copying and adding shortcut, we show that
the growing networks become more robust and efficient through enhancing the
onion-like topological structure on a space. The reasonable constraint for
locating nodes on the perimeter in typical surface growth as a self-propagation
does not affect these properties of the tolerance and the path length.
Moreover, the robustness can be recovered in the random growth damaged by
insistent sequential attacks even without any remedial measures.Comment: 34 pages, 12 figures, 2 table
Improvement of the robustness on geographical networks by adding shortcuts
In a topological structure affected by geographical constraints on liking,
the connectivity is weakened by constructing local stubs with small cycles, a
something of randomness to bridge them is crucial for the robust network
design. In this paper, we numerically investigate the effects of adding
shortcuts on the robustness in geographical scale-free network models under a
similar degree distribution to the original one. We show that a small fraction
of shortcuts is highly contribute to improve the tolerance of connectivity
especially for the intentional attacks on hubs. The improvement is equivalent
to the effect by fully rewirings without geographical constraints on linking.
Even in the realistic Internet topologies, these effects are virtually
examined.Comment: 14 pages, 10 figures, 1 tabl
Optimal Orchestration of Virtual Network Functions
-The emergence of Network Functions Virtualization (NFV) is bringing a set of
novel algorithmic challenges in the operation of communication networks. NFV
introduces volatility in the management of network functions, which can be
dynamically orchestrated, i.e., placed, resized, etc. Virtual Network Functions
(VNFs) can belong to VNF chains, where nodes in a chain can serve multiple
demands coming from the network edges. In this paper, we formally define the
VNF placement and routing (VNF-PR) problem, proposing a versatile linear
programming formulation that is able to accommodate specific features and
constraints of NFV infrastructures, and that is substantially different from
existing virtual network embedding formulations in the state of the art. We
also design a math-heuristic able to scale with multiple objectives and large
instances. By extensive simulations, we draw conclusions on the trade-off
achievable between classical traffic engineering (TE) and NFV infrastructure
efficiency goals, evaluating both Internet access and Virtual Private Network
(VPN) demands. We do also quantitatively compare the performance of our VNF-PR
heuristic with the classical Virtual Network Embedding (VNE) approach proposed
for NFV orchestration, showing the computational differences, and how our
approach can provide a more stable and closer-to-optimum solution
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
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