## Polyhedral Optimization of TensorFlow Computation Graphs

August 29, 2017

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## Memory-efficient Parallel Tensor Decompositions

June 27, 2017

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## A Quantitative and Qualitative Analysis of Tensor Decompositions on Spatiotemporal Data

June 27, 2017

With the recent explosion of systems capable of generating and storing large quantities of GPS data, there is an opportunity to develop novel techniques for analyzing and gaining meaningful insights. In this paper we examine the application of tensor decompositions, a high-dimensional data analysis technique, to georeferenced data sets. Guidance is provided on fitting spatiotemporal data into the tensor model and analyzing the results. We find that tensor decompositions can provide insight and that future research into spatiotemporal tensor decompositions for pattern detection, clustering, and anomaly detection is warranted.

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## Multiresolution Priority Queues

June 27, 2017

Priority queues are container data structures essential to many high performance computing (HPC) applications. In this paper, we introduce multiresolution priority queues, a data structure that improves the performance of the standard heap based implementations by trading off a controllable amount of resolution in the space of priorities. The new data structure can reduce the worst case performance of inserting an element from O(log(n)) to O(log(r)), where n is the number of elements in the queue and r is the number of resolution groups in the priority space. The worst case cost of removing the top element is O(1). When the number of elements in the table is high, the amortized cost to insert an element becomes O(1).

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## A Mathematical Framework for the Detection of Elephant Flows

January 4, 2017

How large is a network flow? Traditionally this question has been addressed by using metrics such as the number of bytes, the transmission rate or the duration of a flow. We reason that a formal mathematical definition of flow size should account for the impact a flow has on the performance of a network: flows that have the largest impact, should have the largest size. In this paper we present a theory of flow ordering that reveals the connection between the abstract concept of flow size and the QoS properties of a network. The theory is generalized to accommodate for the case of partial information, allowing us to model real computer network scenarios such as those found in involuntary lossy environments or voluntary packet sampling protocols (e.g., sFlow). We explore one application of this theory to address the problem of elephant flow detection at very high speed rates. The algorithm uses the information theoretic properties of the problem to help reduce the computational cost by a factor of one thousand.

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