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Graph Odometry [article]

Aaron Dutle, Bill Kay
2012 arXiv   pre-print
We address problem of determining edge weights on a graph using non-backtracking closed walks from a vertex. We show that the weights of all of the edges can be determined from any starting vertex exactly when the graph has minimum degree at least three. We also determine the minimum number of walks required to reveal all edge weights.
arXiv:1211.2151v1 fatcat:txnzhg2lvvav3mlhzrff7nhynu


1959 Political quarterly (London. 1930. Print)  
THE MENTAL HEALTH BILL KAY McDOUGALL “We are in no way disposed to belittle the importance of protecting the public against the possibility of unlawful detention, but we are inclined to think that the  ...  This is why in the new Bill it is stated that “ See Ministry of Health and the Board of Control evidence on the first day to the Royal Commission 1954-57, May 4, 1954, pp. 62-63. 123 KAY McDOUGALL subnormality  ... 
doi:10.1111/j.1467-923x.1959.tb01906.x fatcat:d45sri42tff2dcez4tdt7dk7ce

Neuromorphic Computing is Turing-Complete [article]

Prasanna Date, Catherine Schuman, Bill Kay, Thomas Potok
2021 arXiv   pre-print
Neuromorphic computing is a non-von Neumann computing paradigm that performs computation by emulating the human brain. Neuromorphic systems are extremely energy-efficient and known to consume thousands of times less power than CPUs and GPUs. They have the potential to drive critical use cases such as autonomous vehicles, edge computing and internet of things in the future. For this reason, they are sought to be an indispensable part of the future computing landscape. Neuromorphic systems are
more » ... nly used for spike-based machine learning applications, although there are some non-machine learning applications in graph theory, differential equations, and spike-based simulations. These applications suggest that neuromorphic computing might be capable of general-purpose computing. However, general-purpose computability of neuromorphic computing has not been established yet. In this work, we prove that neuromorphic computing is Turing-complete and therefore capable of general-purpose computing. Specifically, we present a model of neuromorphic computing, with just two neuron parameters (threshold and leak), and two synaptic parameters (weight and delay). We devise neuromorphic circuits for computing all the μ-recursive functions (i.e., constant, successor and projection functions) and all the μ-recursive operators (i.e., composition, primitive recursion and minimization operators). Given that the μ-recursive functions and operators are precisely the ones that can be computed using a Turing machine, this work establishes the Turing-completeness of neuromorphic computing.
arXiv:2104.13983v1 fatcat:7r2ic6oo5vg2zjfhxaeik3ahrq

Improved Bounds for Burning Fence Graphs [article]

Anthony Bonato, Sean English, Bill Kay, Daniel Moghbel
2019 arXiv   pre-print
Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices that are adjacent to a burning vertex. The burning number of a graph G is the minimum number of rounds necessary for each vertex of G to burn. We consider the burning number of the m × n Cartesian grid graphs, written G_m,n. For m = ω(√(n)), the asymptotic
more » ... e of the burning number of G_m,n was determined, but only the growth rate of the burning number was investigated in the case m = O(√(n)), which we refer to as fence graphs. We provide new explicit bounds on the burning number of fence graphs G_c√(n),n, where c > 0.
arXiv:1911.01342v1 fatcat:xtiewm4hcnhtvpgtriwlt3kt44

Contributions to the theory of de Bruijn cycles [article]

Andre Campbell, Anant Godbole, Bill Kay
2013 arXiv   pre-print
A de Bruijn cycle is a cyclic listing of length A, of a collection of A combinatorial objects, so that each object appears exactly once as a set of consecutive elements in the cycle. In this paper, we show the power of de Bruijn's original theorem, namely that the cycles bearing his name exist for n-letter words on a k-letter alphabet for all values of k,n, to prove that we can create de Bruijn cycles for the assignment of elements of [n]=1,2,....,n to the sets in any labeled subposet of the
more » ... lean lattice; de Bruijn's theorem corresponds to the case when the subposet in question consists of a single ground element. The landmark work of Chung, Diaconis, and Graham extended the agenda of finding de Bruijn cycles to possibly the next most natural set of combinatorial objects, namely k-subsets of [n]. In this area, important contributions have been those of Hurlbert and Rudoy. Here we follow the direction of Blanca and Godbole, who proved that, in a suitable encoding, de Bruijn cycles can be created for the subsets of [n of size in the interval [s,t]; 0<=s<t<=n. In this paper we generalize this result to exhibit existence of de Bruijn cycles for words with weight between s and t, where these parameters are suitably restricted.
arXiv:1304.2820v1 fatcat:rinydkd34zcejhhucs2xrz2qea

Covering n-Permutations with (n+1)-Permutations [article]

Taylor Allison, Anant Godbole, Kathryn Hawley, Bill Kay
2012 arXiv   pre-print
Let S_n be the set of all permutations on [n]:=1,2,....,n. We denote by kappa_n the smallest cardinality of a subset A of S_n+1 that "covers" S_n, in the sense that each pi in S_n may be found as an order-isomorphic subsequence of some pi' in A. What are general upper bounds on kappa_n? If we randomly select nu_n elements of S_n+1, when does the probability that they cover S_n transition from 0 to 1? Can we provide a fine-magnification analysis that provides the "probability of coverage" when
more » ... _n is around the level given by the phase transition? In this paper we answer these questions and raise others.
arXiv:1203.5433v1 fatcat:2sgzt2rryfctdg5uzhqij4cdo4

The Iterated Local Model for Social Networks [article]

Anthony Bonato, Huda Chuangpishit, Sean English, Bill Kay, Erin Meger
2019 arXiv   pre-print
arXiv:1903.04523v1 fatcat:3ddtvxcgnvajhecv5myfarhcsy

BitBill: Scalable, Robust, Verifiable Peer-to-Peer Billing for Cloud Computing

Li Chen, Kai Chen
2014 USENIX Workshop on Hot Topics in Cloud Computing  
Our initial results show that BitBill has significantly better scalability (supporting 10x concurrent tenants using the billing service) than the state-of-the-art third-party centralized billing system  ...  Accounting and billing of cloud resources is vital for the operation of cloud service providers and their tenants.  ...  record for billing.  ... 
dblp:conf/hotcloud/Chen014 fatcat:jiwepugwc5gm7dhdnmxpnktwxy

Bounds on the Maximum Number of Minimum Dominating Sets [article]

Samuel Connolly, Zachary Gabor, Anant Godbole, Bill Kay
2013 arXiv   pre-print
arXiv:1308.3210v1 fatcat:k2kd2wv3u5ajrl6nreg3e6devm

On Universal Cycles of Labeled Graphs [article]

Greg Brockman, Bill Kay, Emma E. Snively
2009 arXiv   pre-print
A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops, graphs with multiple edges (with up to m duplications of each edge), directed graphs, hypergraphs, and k-uniform hypergraphs.
arXiv:0808.3610v2 fatcat:uk4zjxgpzbh4fdw7u7622epwye

Hadoop's adolescence

Kai Ren, YongChul Kwon, Magdalena Balazinska, Bill Howe
2013 Proceedings of the VLDB Endowment  
We analyze Hadoop workloads from three di↵erent research clusters from a user-centric perspective. The goal is to better understand data scientists' use of the system and how well the use of the system matches its design. Our analysis suggests that Hadoop usage is still in its adolescence. We see underuse of Hadoop features, extensions, and tools. We see significant diversity in resource usage and application styles, including some interactive and iterative workloads, motivating new tools in
more » ... ecosystem. We also observe significant opportunities for optimizations of these workloads. We find that job customization and configuration are used in a narrow scope, suggesting the future pursuit of automatic tuning systems. Overall, we present the first user-centered measurement study of Hadoop and find significant opportunities for improving its e cient use for data scientists.
doi:10.14778/2536206.2536213 fatcat:nv3gcfkwdrcf7ngpmufppbzyvu

Managing Skew in Hadoop

YongChul Kwon, Kai Ren, Magdalena Balazinska, Bill Howe
2013 IEEE Data Engineering Bulletin  
Challenges in Big Data analytics stem not only from volume, but also variety: extreme diversity in both data types (e.g., text, images, and graphs) and in operations beyond relational algebra (e.g., machine learning, natural language processing, image processing, and graph analysis). As a result, any competitive Big Data system must support some form of parallel user-defined operations (UDOs) that can capture complex data processing tasks over complex data types without changing the core of the
more » ... parallel data processing engine. Hadoop and other popular systems have been shown to provide a convenient programming model for implementing parallel UDOs, but the "black-box" nature of UDOs complicates the automatic load balancing required to achieve parallel scalability. In this paper, we present an overview of some of our recent work that tackles the problem of load imbalance (a.k.a. skew) in parallel UDO evaluation. We first discuss the prevalence of skew in today's applications and clusters. We then discuss our experience with static and dynamic methods for mitigating it.
dblp:journals/debu/KwonRBH13 fatcat:h3acubnr2vhlno4robxbktbaru

The Minimum Number of Edges in Uniform Hypergraphs with Property O [article]

Dwight Duffus, Bill Kay, Vojtech Rodl
2016 arXiv   pre-print
An oriented k-uniform hypergraph (a family of ordered k-sets) has the ordering property (or Property O) if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. We find bounds on the minimum number of edges in a hypergraph with Property O.
arXiv:1608.06621v1 fatcat:ou32ilm4bfc7rnguj5hgqxpf44

Elementary Techniques for Erdos-Ko-Rado-like Theorems [article]

Greg Brockman, Bill Kay
2008 arXiv   pre-print
The well-known Erdos-Ko-Rado Theorem states that if F is a family of k-element subsets of 1,2,...,n (n>2k-1) such that every pair of elements in F has a nonempty intersection, then |F| is at most n-1k-1. The theorem also provides necessary and sufficient conditions for attaining the maximum. We present elementary methods for deriving generalizations of the Erdos-Ko-Rado Theorem on several classes of combinatorial objects. We also extend our results to systems under Hamming intersection.
arXiv:0808.0774v2 fatcat:hsoy3xfoqvgevgxfz2zbtjakc4

On Universal Cycles of Labeled Graphs

Greg Brockman, Bill Kay, Emma E. Snively
2010 Electronic Journal of Combinatorics  
A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with $m$ edges, graphs with loops, graphs with multiple edges (with up to $m$ duplications of each edge), directed graphs, hypergraphs, and $k$-uniform hypergraphs.
doi:10.37236/276 fatcat:3aylmv6xvfg5vd2zyfvb6emobq
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