On the homotopy type of multipath complexes

A multipath in a directed graph is a disjoint union of paths. The multipath complex of a directed graph G is the simplicial complex whose faces are the multipaths of G. We compute Euler characteristics, and associated generating functions, of the multipath complexes of directed graphs from certain families, including transitive tournaments and complete bipartite graphs. We show that if G is a linear graph, polygon, small grid or transitive tournament, then the homotopy type of the multipath complex of G is always contractible or a wedge of spheres. We introduce a new technique for decomposing directed graphs into dynamical regions, which allows us to simplify the homotopy computations

Supporting differentiated classes of resilience in multilayer networks

Services provided over telecommunications networks typically have different resilience requirements and networks need to be able to support different levels of resilience in an efficient manner. This dissertation investigates the problem of supporting differentiated classes of resilience in multilayer networks, including the most stringent resilience class required by critical services. We incorporate an innovative technique of embedding a subnetwork, termed the spine, with comparatively higher availability values at the physical layer. The spine lays a foundation for differentiation between multiple classes of flows that can be leveraged to achieve both high resilience and differentiation. The aim of this research is mainly to explore, design, and evaluate the proposed spine concept model in multilayer networks. The dissertation has four major parts. First, we explore the spine concept through numerical analysis of simple topologies illustrating the potential benefits and the cost considerations of the spine. We develop heuristics algorithms to find suitable spines for a network based on the structural properties of the network topology. Second, an optimization problem is formulated to determine the spine. The problem encompasses estimates of link availability improvements, associated costs, and a total budget. Third, we propose a crosslayer mapping and spine-aware routing design problem with protection given mainly at the lower layer. The problem is designed to transfer lower layer differentiation capability to the upper layer network and flows. We provide two joint routing-mapping optimization formulations and evaluate their performance in a multilayer scenario. Fourth, the joint routing-mapping problem is redesigned with protection given in the upper network layer instead. This will create two isolated logical networks; one mapped to the spine and the other is mapped freely on the network. Flows are assigned a path or path-pair based on their class of resilience. This approach can provide more routing options yielding different availability levels. The joint routing-mapping design problems are formulated as Integer Linear Programming (ILP) models. The goal is to achieve a wider range of availability values across layers and high availability levels for mission-critical services without the need to use higher order protection configurations. The proposed models are evaluated with extensive numerical results using real network topologies

Journal of Telecommunications and Information Technology, 2007, nr 4

kwartalni

Computational approaches for network-based integrative multi-omics analysis

Advances in omics technologies allow for holistic studies into biological systems. These studies rely on integrative data analysis techniques to obtain a comprehensive view of the dynamics of cellular processes, and molecular mechanisms. Network-based integrative approaches have revolutionized multi-omics analysis by providing the framework to represent interactions between multiple different omics-layers in a graph, which may faithfully reflect the molecular wiring in a cell. Here we review network-based multi-omics/multi-modal integrative analytical approaches. We classify these approaches according to the type of omics data supported, the methods and/or algorithms implemented, their node and/or edge weighting components, and their ability to identify key nodes and subnetworks. We show how these approaches can be used to identify biomarkers, disease subtypes, crosstalk, causality, and molecular drivers of physiological and pathological mechanisms. We provide insight into the most appropriate methods and tools for research questions as showcased around the aetiology and treatment of COVID-19 that can be informed by multi-omics data integration. We conclude with an overview of challenges associated with multi-omics network-based analysis, such as reproducibility, heterogeneity, (biological) interpretability of the results, and we highlight some future directions for network-based integration

SDN-based traffic engineering in data centers, Interconnects, and Carrier Networks

Server virtualization and cloud computing have escalated the bandwidth and performance demands on the DCN (data center network). The main challenges in DCN are maximizing network utilization and ensuring fault tolerance to address multiple node-and-link failures. A multitenant and highly dynamic virtualized environment consists of a large number of endstations, leading to a very large number of flows that challenge the scalability of a solution to network throughput maximization. The challenges are scalability, in terms of address learning, forwarding decision convergence, and forwarding state size, as well as flexibility for offloading with VM migration. Geographically distributed data centers are inter-connected through service providers’ carrier network. Service providers offer wide-area network (WAN) connection such as private lines and MPLS circuits between edges of data centers. DC sides of network operators try to maximize the utilization of such defined overlay WAN connection i.e. data center interconnection (DCI), which applies to edges of DC networks. Service provider sides of network operators try to optimize the core of carrier network. Along with the increasing adoption of ROADM, OTN, and packet switching technologies, traditional two-layer IP/MPLS-over-WDM network has evolved into three-layer IP/MPLS-over-OTN-over-DWDM network and once defined overlay topology is now transitioning to dynamic topologies based on on-demand traffic demands. Network operations are thus divided into three physical sub-networks: DCN, overlay DCI, and multi-layer carrier network. Server virtualization, cloud computing and evolving multilayer carrier network challenge traffic engineering to maximize utilization on all physical subnetworks. The emerging software-defined networking (SDN) architecture moves path computation towards a centralized controller, which has global visibility. Carriers indicate a strong preference for SDN to be interoperable between multiple vendors in heterogeneous transport networks. SDN is a natural way to create a unified control plane across multiple administrative divisions. This thesis contributes SDN-based traffic engineering techniques for maximizing network utilization of DCN, DCI, and carrier network. The first part of the thesis focuses on DCN traffic engineering. Traditional forwarding mechanisms using a single path are not able to take advantages of available multiple physical paths. The state-of-the-art MPTCP (Multipath Transmission Control Protocol) solution uses multiple randomly selected paths, but cannot give total aggregated capacity. Moreover, it works as a TCP process, and so does not support other protocols like UDP. To address these issues, this thesis presents a solution using adaptive multipath routing in a Layer-2 network with static (capacity and latency) metrics, which adapts link and path failures. This solution provides innetwork aggregated path capacity to individual flows, as well as scalability and multitenancy, by separating end-station services from the provider’s network. The results demonstrate an improvement of 14% in the worst bisection bandwidth utilization, compared to the MPTCP with 5 sub-flows. The second part of the thesis focuses on DCI traffic engineering. The existing approaches to reservation services provide limited reservation capabilities, e.g. limited connections over links returned by the traceroute over traditional IP-based networks. Moreover, most existing approaches do not address fault tolerance in the event of node or link failures. To address these issues, this thesis presents ECMP-like multipath routing algorithm and forwarding assignment scheme that increase reservation acceptance rate compared to state-of-art reservation frameworks in the WAN-links between data centers, and such reservations can be configured with a limited number of static forwarding rules on switches. Our prototype provides the RESTful web service interface for link-fail event management and re-routes paths for all the affected reservations. In the final part of the thesis, we focused on multi-layer carrier network traffic engineering. New dynamic traffic trends in upper layers (e.g. IP routing) require dynamic configuration of the optical transport to re-direct the traffic, and this in turn requires an integration of multiple administrative control layers. When multiple bandwidth path requests come from different nodes in different layers, a distributed sequential computation cannot optimize the entire network. Most prior research has focused on the two-layer problem, and recent three-layer research studies are limited to the capacity dimensioning problem. In this thesis, we present an optimization model with MILP formulation for dynamic traffic in a three-layer network, especially taking into account the unique technological constraints of the distinct OTN layer. Our experimental results show how unit cost values of different layers affect network cost and parameters in the presence of multiple sets of traffic loads. We also demonstrate the effectiveness of our proposed heuristic approach