34 research outputs found
Walking Through Waypoints
We initiate the study of a fundamental combinatorial problem: Given a
capacitated graph , find a shortest walk ("route") from a source to a destination that includes all vertices specified by a set
: the \emph{waypoints}. This waypoint routing problem
finds immediate applications in the context of modern networked distributed
systems. Our main contribution is an exact polynomial-time algorithm for graphs
of bounded treewidth. We also show that if the number of waypoints is
logarithmically bounded, exact polynomial-time algorithms exist even for
general graphs. Our two algorithms provide an almost complete characterization
of what can be solved exactly in polynomial-time: we show that more general
problems (e.g., on grid graphs of maximum degree 3, with slightly more
waypoints) are computationally intractable
Distributed Consistent Network Updates in SDNs: Local Verification for Global Guarantees
While SDNs enable more flexible and adaptive network operations, (logically)
centralized reconfigurations introduce overheads and delays, which can limit
network reactivity. This paper initiates the study of a more distributed
approach, in which the consistent network updates are implemented by the
switches and routers directly in the data plane. In particular, our approach
leverages concepts from local proof labeling systems, which allows the data
plane elements to locally check network properties, and we show that this is
sufficient to obtain global network guarantees. We demonstrate our approach
considering three fundamental use cases, and analyze its benefits in terms of
performance and fault-tolerance.Comment: Appears in IEEE NCA 201
Maximally Resilient Replacement Paths for a Family of Product Graphs
Modern communication networks support fast path restoration mechanisms which allow to reroute traffic in case of (possibly multiple) link failures, in a completely decentralized manner and without requiring global route reconvergence. However, devising resilient path restoration algorithms is challenging as these algorithms need to be inherently local. Furthermore, the resulting failover paths often have to fulfill additional requirements related to the policy and function implemented by the network, such as the traversal of certain waypoints (e.g., a firewall).
This paper presents local algorithms which ensure a maximally resilient path restoration for a large family of product graphs, including the widely used tori and generalized hypercube topologies. Our algorithms provably ensure that even under multiple link failures, traffic is rerouted to the other endpoint of every failed link whenever possible (i.e. detouring failed links), enforcing waypoints and hence accounting for the network policy. The algorithms are particularly well-suited for emerging segment routing networks based on label stacks
Brief Announcement: Minimizing Congestion in Hybrid Demand-Aware Network Topologies
Emerging reconfigurable optical communication technologies enable demand-aware networks: networks whose static topology can be enhanced with demand-aware links optimized towards the traffic pattern the network serves. This paper studies the algorithmic problem of how to jointly optimize the topology and the routing in such demand-aware networks, to minimize congestion. We investigate this problem along two dimensions: (1) whether flows are splittable or unsplittable, and (2) whether routing on the hybrid topology is segregated or not, i.e., whether or not flows either have to use exclusively either the static network or the demand-aware connections. For splittable and segregated routing, we show that the problem is 2-approximable in general, but APX-hard even for uniform demands induced by a bipartite demand graph. For unsplittable and segregated routing, we show an upper bound of O(log m/ log log m) and a lower bound of ?(log m/ log log m) for polynomial-time approximation algorithms, where m is the number of static links. Under splittable (resp., unsplittable) and non-segregated routing, even for demands of a single source (resp., destination), the problem cannot be approximated better than ?(c_{max}/c_{min}) unless P=NP, where c_{max} (resp., c_{min}) denotes the maximum (resp., minimum) capacity. It is still NP-hard for uniform capacities, but can be solved efficiently for a single commodity and uniform capacities