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Stefan Schmid

Publications and source records attributed to Stefan Schmid.

At least 199 records · Page 11Linked to original sources
arXiv2017

Congestion-Free Rerouting of Flows on DAGs

Changing a given configuration in a graph into another one is known as a re- configuration problem. Such problems have recently received much interest in the context of algorithmic graph theory. We initiate the theoretical study of the following reconfiguration problem: How to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner? This problem finds immediate applications, e.g., in traffic engineering in computer networks. We show that the problem is generally NP-hard already for $k = 2$ flows, which motivates us to study rerouting on a most basic class of flow graphs, namely DAGs. Interestingly, we find that for general $k$, deciding whether an unsplittable multi-commodity flow rerouting schedule exists, is NP-hard even on DAGs. Both NP-hardness proofs are non-trivial. Our main contribution is a polynomial-time (fixed parameter tractable) algorithm to solve the route update problem for a bounded number of flows on DAGs. At the heart of our algorithm lies a novel decomposition of the flow network that allows us to express and resolve reconfiguration dependencies among flows.

cs.DS↗
arXiv2017

Approximate and Incremental Network Function Placement

The virtualization and softwarization of modern computer networks introduces interesting new opportunities for a more flexible placement of network functions and middleboxes (firewalls, proxies, traffic optimizers, virtual switches, etc.). This paper studies approximation algorithms for the incremental deployment of a minimum number of middleboxes at optimal locations, such that capacity constraints at the middleboxes and length constraints on the communication routes are respected. Our main contribution is a new, purely combinatorial and rigorous proof for the submodularity of the function maximizing the number of communication requests that can be served by a given set of middleboxes. Our proof allows us to devise a deterministic approximation algorithm which uses an augmenting path approach to compute the submodular function. This algorithm does not require any changes to the locations of existing middleboxes or the preemption of previously served communication pairs when additional middleboxes are deployed, previously accepted communication pairs just can be handed over to another middlebox. It is hence particularly attractive for incremental deployments.We prove that the achieved polynomial-time approximation bound is optimal, unless P = NP. This paper also initiates the study of a weighted problem variant, in which entire groups of nodes need to communicate via a middlebox (e.g., a multiplexer or a shared object), possibly at different rates. We present an LP relaxation and randomized rounding algorithm for this problem, leveraging an interesting connection to scheduling.

cs.NI↗
arXiv2017

Towards Communication-Aware Robust Topologies

We currently witness the emergence of interesting new network topologies optimized towards the traffic matrices they serve, such as demand-aware datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks (e.g., SplayNets). This paper introduces a formal framework and approach to reason about and design such topologies. We leverage a connection between the communication frequency of two nodes and the path length between them in the network, which depends on the entropy of the communication matrix. Our main contribution is a novel robust, yet sparse, family of network topologies which guarantee an expected path length that is proportional to the entropy of the communication patterns.

cs.NI↗
arXiv2017

Demand-Aware Network Designs of Bounded Degree

Traditionally, networks such as datacenter interconnects are designed to optimize worst-case performance under arbitrary traffic patterns. Such network designs can however be far from optimal when considering the actual workloads and traffic patterns which they serve. This insight led to the development of demand-aware datacenter interconnects which can be reconfigured depending on the workload. Motivated by these trends, this paper initiates the algorithmic study of demand-aware networks (DANs) designs, and in particular the design of bounded-degree networks. The inputs to the network design problem are a discrete communication request distribution, D, defined over communicating pairs from the node set V , and a bound, d, on the maximum degree. In turn, our objective is to design an (undirected) demand-aware network N = (V,E) of bounded-degree d, which provides short routing paths between frequently communicating nodes distributed across N. In particular, the designed network should minimize the expected path length on N (with respect to D), which is a basic measure of the efficiency of the network. We show that this fundamental network design problem exhibits interesting connections to several classic combinatorial problems and to information theory. We derive a general lower bound based on the entropy of the communication pattern D, and present asymptotically optimal network-aware design algorithms for important distribution families, such as sparse distributions and distributions of locally bounded doubling dimensions.

cs.DC↗
arXiv2017

Software-Defined Adversarial Trajectory Sampling

Today's routing protocols critically rely on the assumption that the underlying hardware is trusted. Given the increasing number of attacks on network devices, and recent reports on hardware backdoors this assumption has become questionable. Indeed, with the critical role computer networks play today, the contrast between our security assumptions and reality is problematic. This paper presents Software-Defined Adversarial Trajectory Sampling (SoftATS), an OpenFlow-based mechanism to efficiently monitor packet trajectories, also in the presence of non-cooperating or even adversarial switches or routers, e.g., containing hardware backdoors. Our approach is based on a secure, redundant and adaptive sample distribution scheme which allows us to provably detect adversarial switches or routers trying to reroute, mirror, drop, inject, or modify packets (i.e., header and/or payload). We evaluate the effectiveness of our approach in different adversarial settings, report on a proof-of-concept implementation, and provide a first evaluation of the performance overheads of such a scheme.

cs.NI↗
arXiv2017

Logically Isolated, Actually Unpredictable? Measuring Hypervisor Performance in Multi-Tenant SDNs

Ideally, by enabling multi-tenancy, network virtualization allows to improve resource utilization, while providing performance isolation: although the underlying resources are shared, the virtual network appears as a dedicated network to the tenant. However, providing such an illusion is challenging in practice, and over the last years, many expedient approaches have been proposed to provide performance isolation in virtual networks, by enforcing bandwidth reservations. We in this paper study another source for overheads and unpredictable performance in virtual networks: the hypervisor. The hypervisor is a critical component in multi-tenant environments, but its overhead and influence on performance are hardly understood today. In particular, we focus on OpenFlow-based virtualized Software Defined Networks (vSDNs). Network virtualization is considered a killer application for SDNs: a vSDN allows each tenant to flexibly manage its network from a logically centralized perspective, via a simple API. For the purpose of our study, we developed a new benchmarking tool for OpenFlow control and data planes, enabling high and consistent OpenFlow message rates. Using our tool, we identify and measure controllable and uncontrollable effects on performance and overhead, including the hypervisor technology, the number of tenants as well as the tenant type, as well as the type of OpenFlow messages.

cs.NI↗
arXiv2017

The Many Faces of Graph Dynamics

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a "one fits it all" model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

cs.SI↗
arXiv2017

Reins to the Cloud: Compromising Cloud Systems via the Data Plane

Virtual switches have become popular among cloud operating systems to interconnect virtual machines in a more flexible manner. However, this paper demonstrates that virtual switches introduce new attack surfaces in cloud setups, whose effects can be disastrous. Our analysis shows that these vulnerabilities are caused by: (1) inappropriate security assumptions (privileged virtual switch execution in kernel and user space), (2) the logical centralization of such networks (e.g., OpenStack or SDN), (3) the presence of bi-directional communication channels between data plane systems and the centralized controller, and (4) non-standard protocol parsers. Our work highlights the need to accommodate the data plane(s) in our threat models. In particular, it forces us to revisit today's assumption that the data plane can only be compromised by a sophisticated attacker: we show that compromising the data plane of modern computer networks can actually be performed by a very simple attacker with limited resources only and at low cost (i.e., at the cost of renting a virtual machine in the Cloud). As a case study, we fuzzed only 2\% of the code-base of a production quality virtual switch's packet processor (namely OvS), identifying serious vulnerabilities leading to unauthenticated remote code execution. In particular, we present the "rein worm" which allows us to fully compromise test-setups in less than 100 seconds. We also evaluate the performance overhead of existing mitigations such as ASLR, PIEs, and unconditional stack canaries on OvS. We find that while applying these countermeasures in kernel-space incurs a significant overhead, in user-space the performance overhead is negligible.

cs.NI↗
arXiv2016

WNetKAT: A Weighted SDN Programming and Verification Language

Programmability and verifiability lie at the heart of the software-defined networking paradigm. While OpenFlow and its match-action concept provide primitive operations to manipulate hardware configurations, over the last years, several more expressive network programming languages have been developed. This paper presents WNetKAT, the first network programming language accounting for the fact that networks are inherently weighted, and communications subject to capacity constraints (e.g., in terms of bandwidth) and costs (e.g., latency or monetary costs). WNetKAT is based on a syntactic and semantic extension of the NetKAT algebra. We demonstrate several relevant applications for WNetKAT, including cost- and capacity-aware reachability, as well as quality-of-service and fairness aspects. These applications do not only apply to classic, splittable and unsplittable (s; t)-flows, but also generalize to more complex network functions and service chains. For example, WNetKAT allows to model flows which need to traverse certain waypoint functions, which may change the traffic rate. This paper also shows the relation between the equivalence problem of WNetKAT and the equivalence problem of the weighted finite automata, which implies undecidability of the former. However, this paper also succeeds to prove the decidability of another useful problem, which is sufficient in many practical scnearios: whether an expression equals to 0. Moreover, we initiate the discussion of decidable subsets of the whole language.

cs.NI↗
arXiv2016

Investigating the Potential of the Inter-IXP Multigraph for the Provisioning of Guaranteed End-to-End Services

In this work, we propose utilizing the rich connectivity between IXPs and ISPs for inter-domain path stitching, supervised by centralized QoS brokers. In this context, we highlight a novel abstraction of the Internet topology, i.e., the inter-IXP multigraph composed of IXPs and paths crossing the domains of their shared member ISPs. This can potentially serve as a dense Internet-wide substrate for provisioning guaranteed end-to-end (e2e) services with high path diversity and global IPv4 address space reach. We thus map the IXP multigraph, evaluate its potential, and introduce a rich algorithmic framework for path stitching on such graph structures.

cs.NI↗
arXiv2016

Control Exchange Points: Providing QoS-enabled End-to-End Services via SDN-based Inter-domain Routing Orchestration

This paper presents the vision of the Control Exchange Point (CXP) architectural model. The model is motivated by the inflexibility and ossification of today's inter-domain routing system, which renders critical QoS-constrained end-to-end (e2e) network services difficult or simply impossible to provide. CXPs operate on slices of ISP networks and are built on basic Software Defined Networking (SDN) principles, such as the clean decoupling of the routing control plane from the data plane and the consequent logical centralization of control. The main goal of the architectural model is to provide e2e services with QoS constraints across domains. This is achieved through defining a new type of business relationship between ISPs, which advertise partial paths (so-called pathlets) with specific properties, and the orchestrating role of the CXPs, which dynamically stitch them together and provision e2e QoS. Revenue from value-added services flows from the clients of the CXP to the ISPs participating in the service. The novelty of the approach is the combination of SDN programmability and dynamic path stitching techniques for inter-domain routing, which extends the value proposition of SDN over multiple domains. We first describe the challenges related to e2e service provision with the current inter-domain routing and peering model, and then continue with the benefits of our approach. Subsequently, we describe the CXP model in detail and report on an initial feasibility analysis.

cs.NI↗
arXiv2016

Stitching Inter-Domain Paths over IXPs

Modern Internet applications, from HD video-conferencing to health monitoring and remote control of power-plants, pose stringent demands on network latency, bandwidth and availability. An approach to support such applications and provide inter-domain guarantees, enabling new avenues for innovation, is using centralized inter-domain routing brokers. These entities centralize routing control for mission-critical traffic across domains, working in parallel to BGP. In this work, we propose using IXPs as natural points for stitching inter-domain paths under the control of inter-domain routing brokers. To evaluate the potential of this approach, we first map the global substrate of inter-IXP pathlets that IXP members could offer, based on measurements for 229 IXPs worldwide. We show that using IXPs as stitching points has two useful properties. Up to 91 % of the total IPv4 address space can be served by such inter-domain routing brokers when working in concert with just a handful of large IXPs and their associated ISP members. Second, path diversity on the inter-IXP graph increases by up to 29 times, as compared to current BGP valley-free routing. To exploit the rich path diversity, we introduce algorithms that inter-domain routing brokers can use to embed paths, subject to bandwidth and latency constraints. We show that our algorithms scale to the sizes of the measured graphs and can serve diverse simulated path request mixes. Our work highlights a novel direction for SDN innovation across domains, based on logically centralized control and programmable IXP fabrics.

cs.NI↗
arXiv2016

The Many Faces of Graph Dynamics

The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is known today about the network dynamics: indeed, complex networks in reality are not static, but rather dynamically evolve over time. Our paper is motivated by the empirical observation that network evolution patterns seem far from random, but exhibit structure. Moreover, the specific patterns appear to depend on the network type, contradicting the existence of a "one fits it all" model. However, we still lack observables to quantify these intuitions, as well as metrics to compare graph evolutions. Such observables and metrics are needed for extrapolating or predicting evolutions, as well as for interpolating graph evolutions. To explore the many faces of graph dynamics and to quantify temporal changes, this paper suggests to build upon the concept of centrality, a measure of node importance in a network. In particular, we introduce the notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type. Intuitively, centrality distances reflect the extent to which (non-anonymous) node roles are different or, in case of dynamic graphs, have changed over time, between two graphs. We evaluate the centrality distance approach for five evolutionary models and seven real-world social and physical networks. Our results empirically show the usefulness of centrality distances for characterizing graph dynamics compared to a null-model of random evolution, and highlight the differences between the considered scenarios. Interestingly, our approach allows us to compare the dynamics of very different networks, in terms of scale and evolution speed.

cs.SI↗
arXiv2016

Routing-Verification-as-a-Service (RVaaS): Trustworthy Routing Despite Insecure Providers

Computer networks today typically do not provide any mechanisms to the users to learn, in a reliable manner, which paths have (and have not) been taken by their packets. Rather, it seems inevitable that as soon as a packet leaves the network card, the user is forced to trust the network provider to forward the packets as expected or agreed upon. This can be undesirable, especially in the light of today's trend toward more programmable networks: after a successful cyber attack on the network management system or Software-Defined Network (SDN) control plane, an adversary in principle has complete control over the network. This paper presents a low-cost and efficient solution to detect misbehaviors and ensure trustworthy routing over untrusted or insecure providers, in particular providers whose management system or control plane has been compromised (e.g., using a cyber attack). We propose Routing-Verification-as-a-Service (RVaaS): RVaaS offers clients a flexible interface to query information relevant to their traffic, while respecting the autonomy of the network provider. RVaaS leverages key features of OpenFlow-based SDNs to combine (passive and active) configuration monitoring, logical data plane verification and actual in-band tests, in a novel manner.

cs.NI↗
arXiv2016

Convergence of Even Simpler Robots without Location Information

The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that convergence problems can even be solved for very weak, \emph{oblivious} robots: robots which cannot maintain state from one round to the next. The oblivious robot model is hence attractive from a self-stabilization perspective, where state is subject to adversarial manipulation. However, to the best of our knowledge, all existing robot convergence protocols rely on the assumption that robots, despite being "weak", can measure distances. We in this paper initiate the study of convergence protocols for even simpler robots, called \emph{monoculus robots}: robots which cannot measure distances. In particular, we introduce two natural models which relax the assumptions on the robots' cognitive capabilities: (1) a Locality Detection ($\mathcal{LD}$) model in which a robot can only detect whether another robot is closer than a given constant distance or not, (2) an Orthogonal Line Agreement ($\mathcal{OLA}$) model in which robots only agree on a pair of orthogonal lines (say North-South and West-East, but without knowing which is which). The problem turns out to be non-trivial, and simple median and angle bisection strategies can easily increase the distances among robots (e.g., the area of the enclosing convex hull) over time. Our main contribution are deterministic self-stabilizing convergence algorithms for these two models, together with a complexity analysis. We also show that in some sense, the assumptions made in our models are minimal: by relaxing the assumptions on the \textit{monoculus robots} further, we run into impossibility results.

cs.DC↗
arXiv2016

Transiently Consistent SDN Updates: Being Greedy is Hard

The software-defined networking paradigm introduces interesting opportunities to operate networks in a more flexible, optimized, yet formally verifiable manner. Despite the logically centralized control, however, a Software-Defined Network (SDN) is still a distributed system, with inherent delays between the switches and the controller. Especially the problem of changing network configurations in a consistent manner, also known as the consistent network update problem, has received much attention over the last years. In particular, it has been shown that there exists an inherent tradeoff between update consistency and speed. This paper revisits the problem of updating an SDN in a transiently consistent, loop-free manner. First, we rigorously prove that computing a maximum (greedy) loop-free network update is generally NP-hard; this result has implications for the classic maximum acyclic subgraph problem (the dual feedback arc set problem) as well. Second, we show that for special problem instances, fast and good approximation algorithms exist.

cs.NI↗
arXiv2016

PRI: Privacy Preserving Inspection of Encrypted Network Traffic

Traffic inspection is a fundamental building block of many security solutions today. For example, to prevent the leakage or exfiltration of confidential insider information, as well as to block malicious traffic from entering the network, most enterprises today operate intrusion detection and prevention systems that inspect traffic. However, the state-of-the-art inspection systems do not reflect well the interests of the different involved autonomous roles. For example, employees in an enterprise, or a company outsourcing its network management to a specialized third party, may require that their traffic remains confidential, even from the system administrator. Moreover, the rules used by the intrusion detection system, or more generally the configuration of an online or offline anomaly detection engine, may be provided by a third party, e.g., a security research firm, and can hence constitute a critical business asset which should be kept confidential. Today, it is often believed that accounting for these additional requirements is impossible, as they contradict efficiency and effectiveness. We in this paper explore a novel approach, called Privacy Preserving Inspection (PRI), which provides a solution to this problem, by preserving privacy of traffic inspection and confidentiality of inspection rules and configurations, and e.g., also supports the flexible installation of additional Data Leak Prevention (DLP) rules specific to the company.

cs.CR↗
arXiv2016

Service Chain and Virtual Network Embeddings: Approximations using Randomized Rounding

The SDN and NFV paradigms enable novel network services which can be realized and embedded in a flexible and rapid manner. For example, SDN can be used to flexibly steer traffic from a source to a destination through a sequence of virtualized middleboxes, in order to realize so-called service chains. The service chain embedding problem consists of three tasks: admission control, finding suitable locations to allocate the virtualized middleboxes and computing corresponding routing paths. This paper considers the offline batch embedding of multiple service chains. Concretely, we consider the objectives of maximizing the profit by embedding an optimal subset of requests or minimizing the costs when all requests need to be embedded. Interestingly, while the service chain embedding problem has recently received much attention, so far, only non- polynomial time algorithms (based on integer programming) as well as heuristics (which do not provide any formal guarantees) are known. This paper presents the first polynomial time service chain approximation algorithms both for the case with admission and without admission control. Our algorithm is based on a novel extension of the classic linear programming and randomized rounding technique, which may be of independent interest. In particular, we show that our approach can also be extended to more complex service graphs, containing cycles or sub-chains, hence also providing new insights into the classic virtual network embedding problem.

cs.NI↗