Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.

/pdf/pregel-a-system-for-large-scale-graph-processing-30lgjenxxg.pdf

Pregel: a system for large-scale graph processing

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

Computational geometry

Matrix transpose is a fundamental communication operation which is not dealt with optimally by general purpose routing schemes. For two dimensional meshes, the first optimal routing schedule is given. The strategy is simple enough to be implemented, but details of the available hardware are not favorable. However, alternative algorithms, designed along the same lines, give an improvement on the Intel Paragon.

Matrix Transpose on Meshes: Theory and Practice

We consider the problem of Breadth First Search (BFS) traversal on massive sparse undirected graphs. Despite the existence of simple linear time algorithms in the RAM model, it was considered non-viable for massive graphs because of the I/O cost it incurs. Munagala and Ranade [29] and later Mehlhorn and Meyer [27] gave efficient algorithms (refered to as MR BFS and MM BFS, respectively) for computing BFS level decompositions in an external memory model. Ajwani et al. [3] implemented MR BFS and the randomized variant of MM BFS using the external memory library STXXL and gave a comparative study of the two algorithms on various graph classes. In this paper, we review and extend that result demonstrating the effectiveness and viability of the BFS implementations on various other synthetic and real world benchmarks. Furthermore, we present the implementation of the deterministic variant of MM BFS and show that in most cases, it outperforms the randomized variant.

https://www.dis.uniroma1.it/~challenge9/papers/ajwani.pdf

Breadth First Search on Massive Graphs.

Multisplit is a broadly useful parallel primitive that permutes its input data into contiguous buckets or bins, where the function that categorizes an element into a bucket is provided by the programmer. Due to the lack of an efficient multisplit on GPUs, programmers often choose to implement multisplit with a sort. One way is to first generate an auxiliary array of bucket IDs and then sort input data based on it. In case smaller indexed buckets possess smaller valued keys, another way for multisplit is to directly sort input data. Both methods are inefficient and require more work than necessary: the former requires more expensive data movements while the latter spends unnecessary effort in sorting elements within each bucket. In this work, we provide a parallel model and multiple implementations for the multisplit problem. Our principal focus is multisplit for a small (up to 256) number of buckets. We use warp-synchronous programming models and emphasize warp-wide communications to avoid branch divergence and reduce memory usage. We also hierarchically reorder input elements to achieve better coalescing of global memory accesses. On a GeForce GTX 1080 GPU, we can reach a peak throughput of 18.93 Gkeys/s (or 11.68 Gpairs/s) for a key-only (or key-value) multisplit. Finally, we demonstrate how multisplit can be used as a building block for radix sort. In our multisplit-based sort implementation, we achieve comparable performance to the fastest GPU sort routines, sorting 32-bit keys (and key-value pairs) with a throughput of 3.0 G keys/s (and 2.1 Gpair/s).

GPU Multisplit: an extended study of a parallel algorithm

We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially n nodes and O(n) edges and monotone update sequences of either �(n) edge insertions or �(n) edge deletions, we prove an amortized high-probability bound of O(n/B 2/3 + sort(n) · log B) I/Os per update. In contrast, the currently best approach for static BFS on sparse undirected graphs requires (n/B 1/2 + sort(n)) I/Os.

/pdf/on-dynamic-breadth-first-search-in-external-memory-1ppb2z76ec.pdf

Ulrich Meyer

Papers

Matrix Transpose on Meshes: Theory and Practice

Breadth First Search on Massive Graphs.

GPU Multisplit: an extended study of a parallel algorithm

On dynamic breadth-first search in external-memory

I/O-Efficient Undirected Shortest Paths