An optimally data efficient isomorphism inference algorithm

The time, space, and data complexity of an optimally data efficient isomorphism identification algorithm are presented. The data complexity, the amount of data required for an inference algorithm to terminate, is analyzed and shown to be the minimum possible for all possible isomorphism inference algorithms. The minimum data requirement is shown to be ⌈log2 (n)⌉, and a method for constructing this minimal sequence of data is presented. The average data requirement is shown to be approximately 2 log2(n). The time complexity is O(n2log2(n)) and the space requirement is O(n2

Streaming Graph Challenge: Stochastic Block Partition

An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard, but existing relaxation methods provide reasonable approximate solutions that can be scaled for large graphs. Competitive benchmarks and challenges have proven to be an effective means to advance state-of-the-art performance and foster community collaboration. This paper describes a graph partition challenge with a baseline partition algorithm of sub-quadratic complexity. The algorithm employs rigorous Bayesian inferential methods based on a statistical model that captures characteristics of the real-world graphs. This strong foundation enables the algorithm to address limitations of well-known graph partition approaches such as modularity maximization. This paper describes various aspects of the challenge including: (1) the data sets and streaming graph generator, (2) the baseline partition algorithm with pseudocode, (3) an argument for the correctness of parallelizing the Bayesian inference, (4) different parallel computation strategies such as node-based parallelism and matrix-based parallelism, (5) evaluation metrics for partition correctness and computational requirements, (6) preliminary timing of a Python-based demonstration code and the open source C++ code, and (7) considerations for partitioning the graph in streaming fashion. Data sets and source code for the algorithm as well as metrics, with detailed documentation are available at GraphChallenge.org.Comment: To be published in 2017 IEEE High Performance Extreme Computing Conference (HPEC

Multi-capacity bin packing with dependent items and its application to the packing of brokered workloads in virtualized environments

Providing resource allocation with performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, in which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. Existing resource allocation solutions either assume that applications manage their data transfer between their virtualized resources, or that cloud providers manage their internal networking resources. With the increased prevalence of brokerage services in cloud platforms, there is a need for resource allocation solutions that provides predictability guarantees in settings, in which neither application scheduling nor cloud provider resources can be managed/controlled by the broker. This paper addresses this problem, as we define the Network-Constrained Packing (NCP) problem of finding the optimal mapping of brokered resources to applications with guaranteed performance predictability. We prove that NCP is NP-hard, and we define two special instances of the problem, for which exact solutions can be found efficiently. We develop a greedy heuristic to solve the general instance of the NCP problem , and we evaluate its efficiency using simulations on various application workloads, and network models.This work was done while author was at Boston University. It was partially supported by NSF CISE awards #1430145, #1414119, #1239021 and #1012798. (1430145 - NSF CISE; 1414119 - NSF CISE; 1239021 - NSF CISE; 1012798 - NSF CISE

Network-constrained packing of brokered workloads in virtualized environments

Providing resource allocation with performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, in which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. Existing resource allocation solutions either assume that applications manage their data transfer between their virtualized resources, or that cloud providers manage their internal networking resources.With the increased prevalence of brokerage services in cloud platforms, there is a need for resource allocation solutions that provides predictability guarantees in settings, in which neither application scheduling nor cloud provider resources can be managed/controlled by the broker. This paper addresses this problem, as we define the Network-Constrained Packing (NCP)problem of finding the optimal mapping of brokered resources to applications with guaranteed performance predictability. We prove that NCP is NP-hard, and we define two special instances of the problem, for which exact solutions can be found efficiently. We develop a greedy heuristic to solve the general instance of the NCP problem, and we evaluate its efficiency using simulations on various application workloads, and network models.This work is supported by NSF CISE CNS Award #1347522, # 1239021, # 1012798