Semi-Streaming Algorithms for Annotated Graph Streams

Considerable effort has been devoted to the development of streaming algorithms for analyzing massive graphs. Unfortunately, many results have been negative, establishing that a wide variety of problems require $\Omega(n^2)$ space to solve. One of the few bright spots has been the development of semi-streaming algorithms for a handful of graph problems -- these algorithms use space $O(n\cdot\text{polylog}(n))$. In the annotated data streaming model of Chakrabarti et al., a computationally limited client wants to compute some property of a massive input, but lacks the resources to store even a small fraction of the input, and hence cannot perform the desired computation locally. The client therefore accesses a powerful but untrusted service provider, who not only performs the requested computation, but also proves that the answer is correct. We put forth the notion of semi-streaming algorithms for annotated graph streams (semi-streaming annotation schemes for short). These are protocols in which both the client's space usage and the length of the proof are $O(n \cdot \text{polylog}(n))$. We give evidence that semi-streaming annotation schemes represent a substantially more robust solution concept than does the standard semi-streaming model. On the positive side, we give semi-streaming annotation schemes for two dynamic graph problems that are intractable in the standard model: (exactly) counting triangles, and (exactly) computing maximum matchings. The former scheme answers a question of Cormode. On the negative side, we identify for the first time two natural graph problems (connectivity and bipartiteness in a certain edge update model) that can be solved in the standard semi-streaming model, but cannot be solved by annotation schemes of "sub-semi-streaming" cost. That is, these problems are just as hard in the annotations model as they are in the standard model.Comment: This update includes some additional discussion of the results proven. The result on counting triangles was previously included in an ECCC technical report by Chakrabarti et al. available at http://eccc.hpi-web.de/report/2013/180/. That report has been superseded by this manuscript, and the CCC 2015 paper "Verifiable Stream Computation and Arthur-Merlin Communication" by Chakrabarti et a

Sensor Search Techniques for Sensing as a Service Architecture for The Internet of Things

The Internet of Things (IoT) is part of the Internet of the future and will comprise billions of intelligent communicating "things" or Internet Connected Objects (ICO) which will have sensing, actuating, and data processing capabilities. Each ICO will have one or more embedded sensors that will capture potentially enormous amounts of data. The sensors and related data streams can be clustered physically or virtually, which raises the challenge of searching and selecting the right sensors for a query in an efficient and effective way. This paper proposes a context-aware sensor search, selection and ranking model, called CASSARAM, to address the challenge of efficiently selecting a subset of relevant sensors out of a large set of sensors with similar functionality and capabilities. CASSARAM takes into account user preferences and considers a broad range of sensor characteristics, such as reliability, accuracy, location, battery life, and many more. The paper highlights the importance of sensor search, selection and ranking for the IoT, identifies important characteristics of both sensors and data capture processes, and discusses how semantic and quantitative reasoning can be combined together. This work also addresses challenges such as efficient distributed sensor search and relational-expression based filtering. CASSARAM testing and performance evaluation results are presented and discussed.Comment: IEEE sensors Journal, 2013. arXiv admin note: text overlap with arXiv:1303.244

The orbital motion of the Quintuplet cluster - a common origin for the Arches and Quintuplet clusters?

We investigate the orbital motion of the Quintuplet cluster near the Galactic center with the aim of constraining formation scenarios of young, massive star clusters in nuclear environments. Three epochs of adaptive optics high-angular resolution imaging with Keck/NIRC2 and VLT/NACO were obtained over a time baseline of 5.8 years, delivering an astrometric accuracy of 0.5-1 mas/yr. Proper motions were derived in the cluster reference frame and were used to distinguish cluster members from the majority of field stars. Fitting the cluster and field proper motion distributions with 2D gaussian models, we derive the orbital motion of the cluster for the first time. The Quintuplet is moving with a 2D velocity of 132 +/- 15 km/s with respect to the field along the Galactic plane, which yields a 3D orbital velocity of 167 +/- 15 km/s when combined with the previously known radial velocity. From a sample of 119 stars measured in three epochs, we derive an upper limit to the velocity dispersion in the core of the Quintuplet cluster of sigma_1D < 10 km/s. Knowledge of the three velocity components of the Quintuplet allows us to model the cluster orbit in the potential of the inner Galaxy. Comparing the Quintuplet's orbit with the Arches orbit, we discuss the possibility that both clusters originated in the same area of the central molecular zone. [abridged]Comment: 40 pages, 12 figures, accepted for publication in Ap

Equivalence Classes and Conditional Hardness in Massively Parallel Computations

The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the one cycle vs. two cycles problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., P ? NP), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems. In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N)), and some standard classes concerning space complexity, namely L and NL, and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model