Software-defined networking (SDN) allows operators to control the behavior of a network by programatically managing the forwarding rules installed on switches. However, as is common in distributed systems, it can be difficult to ensure that certain consistency properties are preserved during periods of reconfiguration. The widely-accepted notion of PER-PACKET CONSISTENCY requires every packet to be forwarded using the new configuration or the old configuration, but not a mixture of the two. If switches can be updated in some (partial) order which guarantees that per-packet consistency is preserved, we call this order a CONSISTENT ORDER UPDATE. In particular, switches that are incomparable in this order can be updated in parallel. We call a consistent order update OPTIMAL if it allows maximal parallelism. This paper presents a polynomial-time algorithm for finding an optimal consistent order update. This contrasts with other recent results in the literature, which show that for other classes of properties (e.g., loop-freedom and waypoint enforcement), the optimal update problem is NP-complete.
There are various approaches for producing a sequence of switch updates guaranteed to respect certain path-based consistency properties (e.g., properties representable using temporal logic, etc.). For example, use counter-example guided search and incremental LTL model checking, FLIP @cite_9 uses integer linear programming, and CCG @cite_5 uses custom reachability-based graph algorithms. Other works such as Dionysus @cite_7 , zUpdate @cite_6 , and , seek to perform updates with respect to quantitative properties.
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It is critical to ensure that network policy remains consistent during state transitions. However, existing techniques impose a high cost in update delay, and or FIB space. We propose the Customizable Consistency Generator (CCG), a fast and generic framework to support customizable consistency policies during network updates. CCG effectively reduces the task of synthesizing an update plan under the constraint of a given consistency policy to a verification problem, by checking whether an update can safely be installed in the network at a particular time, and greedily processing network state transitions to heuristically minimize transition delay. We show a large class of consistency policies are guaranteed by this greedy heuristic alone; in addition, CCG makes judicious use of existing heavier-weight network update mechanisms to provide guarantees when necessary. As such, CCG nearly achieves the "best of both worlds": the efficiency of simply passing through updates in most cases, with the consistency guarantees of more heavyweight techniques. Mininet and physical testbed evaluations demonstrate CCG's capability to achieve various types of consistency, such as path and bandwidth properties, with zero switch memory overhead and up to a 3× delay reduction compared to previous solutions. This paper introduces a novel real-time algorithm for facial landmark tracking. Compared to detection, tracking has both additional challenges and opportunities. Arguably the most important aspect in this domain is updating a tracker’s models as tracking progresses, also known as incremental (face) tracking. While this should result in more accurate localisation, how to do this online and in real time without causing a tracker to drift is still an important open research question. We address this question in the cascaded regression framework, the state-of-the-art approach for facial landmark localisation. Because incremental learning for cascaded regression is costly, we propose a much more efficient yet equally accurate alternative using continuous regression. More specifically, we first propose cascaded continuous regression (CCR) and show its accuracy is equivalent to the Supervised Descent Method. We then derive the incremental learning updates for CCR (iCCR) and show that it is an order of magnitude faster than standard incremental learning for cascaded regression, bringing the time required for the update from seconds down to a fraction of a second, thus enabling real-time tracking. Finally, we evaluate iCCR and show the importance of incremental learning in achieving state-of-the-art performance. Code for our iCCR is available from http: www.cs.nott.ac.uk psxes1. It is well known that causal consistency is more expensive to implement than eventual consistency due to its requirement of dependency tracking and checking for causality. To close the performance gap between the two consistency models, we propose a new protocol that implements causal consistency for both partitioned and replicated data stores. Our protocol trades the visibility latency of updates across different client sessions for higher throughput. An update, either from a local client or a remote replica, is only visible to other clients after it is replicated by all replicas. As a result, a read operation never introduces dependencies to its client session. Only update operations introduce dependencies. By exploiting the transitive property of causality and total order update propagation, an update always has at most one dependency. By reducing the number of tracked dependencies and the number of messages for dependency checking down to one, we believe our protocol can provide causal consistency with similar cost to eventual consistency. This paper examines techniques for finding falsifying trajectories of hybrid systems using an approach that we call trajectory splicing. Many formal verification techniques for hybrid systems, including flowpipe construction, can identify plausible abstract counterexamples for property violations. However, there is often a gap between the reported abstract counterexamples and the concrete system trajectories. Our approach starts with a candidate sequence of disconnected trajectory segments, each segment lying inside a discrete mode. However, such disconnected segments do not form concrete violations due to the gaps that exist between the ending state of one segment and the starting state of the subsequent segment. Therefore, trajectory splicing uses local optimization to minimize the gap between these segments, effectively splicing them together to form a concrete trajectory. We demonstrate the use of our approach for falsifying safety properties of hybrid systems using standard optimization techniques. As such, our approach is not restricted to linear systems. We compare our approach with other falsification approaches including uniform random sampling and a robustness guided falsification approach used in the tool S-Taliro. Our preliminary evaluation clearly shows the potential of our approach to search for candidate trajectory segments and use them to find concrete property violations.