Greedy algorithms are practitioners’ best friends—they are intuitive, are simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power. Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. Armed with this primitive, we then adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to p-system constraint problems. Our method yields efficient algorithms that run in a logarithmic number of rounds while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or p-system constraints.

Fast Greedy Algorithms in MapReduce and Streaming

We present Hubble, a system that operates continuously to find Internet reachability problems in which routes exist to a destination but packets are unable to reach the destination. Hubble monitors at a 15 minute granularity the data-path to prefixes that cover 89% of the Internet's edge address space. Key enabling techniques include a hybrid passive/active monitoring approach and the synthesis of multiple information sources that include historical data.

With these techniques, we estimate that Hubble discovers 85% of the reachability problems that would be found with a pervasive probing approach, while issuing only 5.5% as many probes. We also present the results of a three week study conducted with Hubble. We find that the extent of reachability problems, both in number and duration, is much greater than we expected, with problems persisting for hours and even days, and many of the problems do not correlate with BGP updates. In many cases, a multi-homed AS is reachable through one provider, but probes through another terminate; using spoofed packets, we isolated the direction of failure in 84% of cases we analyzed and found all problems to be exclusively on the forward path from the provider to the destination. A snapshot of the problems Hubble is currently monitoring can be found at http://hubble.cs.washington.edu.

/pdf/studying-black-holes-in-the-internet-with-hubble-24kgq4luwf.pdf

Studying black holes in the internet with Hubble

A transform domain-based anomaly detection approach to network-wide traffic

Natural and human factors cause Internet outages---from big events like Hurricane Sandy in 2012 and the Egyptian Internet shutdown in Jan. 2011 to small outages every day that go unpublicized. We describe Trinocular, an outage detection system that uses active probing to understand reliability of edge networks. Trinocular is principled: deriving a simple model of the Internet that captures the information pertinent to outages, and populating that model through long-term data, and learning current network state through ICMP probes. It is parsimonious, using Bayesian inference to determine how many probes are needed. On average, each Trinocular instance sends fewer than 20 probes per hour to each /24 network block under study, increasing Internet "background radiation" by less than 0.7%. Trinocular is also predictable and precise: we provide known precision in outage timing and duration. Probing in rounds of 11 minutes, we detect 100% of outages one round or longer, and estimate outage duration within one-half round. Since we require little traffic, a single machine can track 3.4M /24 IPv4 blocks, all of the Internet currently suitable for analysis. We show that our approach is significantly more accurate than the best current methods, with about one-third fewer false conclusions, and about 30% greater coverage at constant accuracy. We validate our approach using controlled experiments, use Trinocular to analyze two days of Internet outages observed from three sites, and re-analyze three years of existing data to develop trends for the Internet.

/pdf/trinocular-understanding-internet-reliability-through-4z4hyhgwkm.pdf

Trinocular: understanding internet reliability through adaptive probing

Skyline queries are a popular way to obtain preferred answers from the database by providing only the orderings of attribute values. The result of a skyline query consists of those input tuples for which there is no input tuple having better or equal values in all the attributes and a better value in at least one attribute. In this article, we summarize the basic notions and properties of skyline queries, and discuss their extensions and generalizations. In particular, we consider skyline algorithms and skyline cardinality issues.

/pdf/skyline-queries-front-and-back-1p3jsyfj0i.pdf

Skyline queries, front and back

To maintain high availability in the face of changing network conditions, network operators must quickly detect, identify, and react to events that cause network disruptions. One way to accomplish this goal is to monitor routing dynamics, by analyzing routing update streams collected from routers. Existing monitoring approaches typically treat streams of routing updates from different routers as independent signals, and report only the "loud" events (i.e., events that involve large volume of routing messages). In this paper, we examine BGP routing data from all routers in the Abilene backbone for six months and correlate them with a catalog of all known disruptions to its nodes and links. We find that many important events are not loud enough to be detected from a single stream. Instead, they become detectable only when multiple BGP update streams are simultaneously examined. This is because routing updates exhibit network-wide dependencies.This paper proposes using network-wide analysis of routing information to diagnose (i.e., detect and identify) network disruptions. To detect network disruptions, we apply a multivariate analysis technique on dynamic routing information, (i.e., update traffic from all the Abilene routers) and find that this technique can detect every reported disruption to nodes and links within the network with a low rate of false alarms. To identify the type of disruption, we jointly analyze both the network-wide static configuration and details in the dynamic routing updates; we find that our method can correctly explain the scenario that caused the disruption. Although much work remains to make network-wide analysis of routing data operationally practical, our results illustrate the importance and potential of such an approach.

/pdf/diagnosing-network-disruptions-with-network-wide-analysis-2o1razex0e.pdf

Diagnosing network disruptions with network-wide analysis

The study of skylines and their variants has received considerable attention in recent years. Skylines are essentially sets of most interesting (undominated) tuples in a database. However, since the skyline is often very large, much research effort has been devoted to identifying a smaller subset of (say k) “representative skyline” points. Several different definitions of representative skylines have been considered. Most of these formulations are intuitive in that they try to achieve some kind of clustering “spread” over the entire skyline, with k points. In this work, we take a more principled approach in defining the representative skyline objective. One of our main contributions is to formulate the problem of displaying k representative skyline points such that the probability that a random user would click on one of them is maximized.

Jim Xu

Papers

Diagnosing network disruptions with network-wide analysis

Representative skylines using threshold-based preference distributions