Klaus-Tycho Foerster

A Walk in the Clouds: Routing Through VNFs on Bidirected Networks

The virtualization of network functions enables innovative new network services which can be deployed quickly and at low cost on (distributed) cloud computing infrastructure. This paper initiates the algorithmic study of the fundamental underlying problem of how to efficiently route traffic through a given set of Virtualized Network Functions (VNFs). We are given a link-capacitated network \(G=(V,E)\), a source-destination pair \((s,t)\in V^2\) and a set of waypoints \(\mathscr {W} \subset V\) (the VNFs). In particular, we consider the practically relevant but rarely studied case of bidirected networks. The objective is to find a (shortest) route from s to t such that all waypoints are visited. We show that the problem features interesting connections to classic combinatorial problems, present different algorithms, and derive hardness results.

Run, Walk, Crawl: Towards Dynamic Link Capacities

Fiber optic cables are the workhorses of todays Internet services. Operators spend millions of dollars to purchase, lease and maintain their optical backbone, making the efficiency of fiber essential to their business. In this work, we make a case for adapting the capacity of optical links based on their signal-to-noise ratio (SNR). We show two immediate benefits of this by analyzing the SNR of over 2000 links in an optical backbone over a period of 2.5 years. First, the capacity of 80% of IP links can be augmented by 75% or more, leading to an overall capacity gain of 145 Tbps in a large optical backbone in North America. Second, at least 25% of link failures are caused by SNR degradation, not complete loss-of-light, highlighting the opportunity to replace link failures by link flaps wherein the capacity is adjusted according to the new SNR. Given these benefits, we identify the disconnect between current optical and networking infrastructure which hinders the deployment of dynamic capacity links in wide area networks (WANs). To bridge this gap, we propose a graph abstraction that enables existing traffic engineering algorithms to benefit from dynamic link capacities. We evaluate the feasibility of dynamic link capacities using a small testbed and simulate the throughput gains from deploying our approach.

Local Fast Failover Routing With Low Stretch

Network failures are frequent and disruptive, and can significantly reduce the throughput even in highly connected and regular networks such as datacenters. While many modern networks support some kind of local fast failover to quickly reroute flows encountering link failures to new paths, employing such mechanisms is known to be non-trivial, as conditional failover rules can only depend on local failure information. While over the last years, important insights have been gained on how to design failover schemes providing high resiliency, existing approaches have the shortcoming that the resulting failover routes may be unnecessarily long, i.e., they have a large stretch compared to the original route length. This is a serious drawback, as long routes entail higher latencies and introduce loads, which may cause the rerouted flows to interfere with existing flows and harm throughput. This paper presents the first deterministic local fast failover algorithms providing provable resiliency and failover route lengths, even in the presence of many concurrent failures. We present stretch-optimal failover algorithms for different network topologies, including multi-dimensional grids, hypercubes and Clos networks, as they are frequently deployed in the context of HPC clusters and datacenters. We show that the computed failover routes are optimal in the sense that no failover algorithm can provide shorter paths for a given number of link failures.

Multi-agent Pathfinding with n Agents on Graphs with n Vertices: Combinatorial Classification and Tight Algorithmic Bounds

We investigate the multi-agent pathfinding (MAPF) problem with n agents on graphs with n vertices: Each agent has a unique start and goal vertex, with the objective of moving all agents in parallel movements to their goal s.t. each vertex and each edge may only be used by one agent at a time. We give a combinatorial classification of all graphs where this problem is solvable in general, including cases where the solvability depends on the initial agent placement.

Charting the Algorithmic Complexity of Waypoint Routing

Modern computer networks support interesting new routing models in which traffic flows from a source sto a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network functions (VNFs), to create innovative network services like service chains or segment routing. While the benefits and technological challenges of providing such routing models have been articulated and studied intensively over the last years, less is known about the underlying algorithmic traffic routing problems. The goal of this paper is to provide the network community with an overview of algorithmic techniques for waypoint routing and also inform about limitations due to computational hardness. In particular, we put the waypoint routing problem into perspective with respect to classic graph theoretical problems. For example, we find that while computing a shortest path from a source s to a destination t is simple (e.g., using Dijkstras algorithm), the problem of finding a shortest route from s to t via a single waypoint already features a deep combinatorial structure.

Wireless Evacuation on m Rays with k Searchers

We study the online problem of evacuating k robots on m concurrent rays to a single unknown exit. All k robots start on the same point \(s\), not necessarily on the junction \(j\) of the m rays, move at unit speed, and can communicate wirelessly. The goal is to minimize the competitive ratio, i.e., the ratio between the time it takes to evacuate all robots to the exit and the time it would take if the location of the exit was known in advance, on a worst-case instance.