Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures最新文献

{"title":"Fast Distributed Algorithms for Connectivity and MST in Large Graphs","authors":"Gopal Pandurangan, Peter Robinson, Michele Scquizzato","doi":"10.1145/2935764.2935785","DOIUrl":"https://doi.org/10.1145/2935764.2935785","url":null,"abstract":"Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n gg k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in ~O(n/k2) rounds (~O notation hides a polylog(n) factor and an additive polylog(n) term). This improves over the best previously known bound of ~O(n/k) [Klauck et al., SODA 2015], and is optimal (up to a polylogarithmic factor) in view of an existing lower bound of ~Ω(n/k2). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. We then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take ~O(n/k2) rounds, and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of ~Ω(n/k2) for many graph verification problems using lower bounds in random-partition communication complexity.","PeriodicalId":346939,"journal":{"name":"Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132812732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Family Holiday Gathering Problem or Fair and Periodic Scheduling of Independent Sets","authors":"A. Amir, O. Kapah, T. Kopelowitz, M. Naor, E. Porat","doi":"10.1145/2935764.2935788","DOIUrl":"https://doi.org/10.1145/2935764.2935788","url":null,"abstract":"We introduce the Holiday Gathering Problem which models the difficulty in scheduling non-interfering transmissions in (wireless) networks. Our goal is to schedule transmission rounds so that the antennas that transmit in a given round will not interfere with each other, i.e. all of the other antennas that can interfere will not transmit in that round, while minimizing the number of consecutive rounds in which antennas do not transmit. Following a long tradition in Computer Science, we introduce the problem by an intuitive story. Assume we live in a perfect world where families enjoy being together. Consequently, parents, whose children are in a monogamous relation, would like to have all their children at home for the holiday meal (i.e. there is a special pleasure gained by hosting all the children simultaneously and they wish to have this event occur as frequently as possible). However, the conflict is that the in-laws would also be happiest if all their children come to them. Our goal can be described as scheduling an infinite sequence of \"guest lists\" in a distributed setting so that each child knows where it will spend the holiday. The holiday gathering problem is closely related to several classical problems in computer science, such as the dining philosophers problem on a general graph and periodic scheduling. The process of the scheduling should be done with no further communication after initialization, by using a small amount of local data. The result should minimize the number of consecutive holidays where the family is not together. In a good sequence this number depends on local properties of the parents (e.g., their number of children). Furthermore, solutions that are periodic, i.e. a gathering occurs every fixed number of rounds, are useful for maintaining a small amount of information at each node and reducing the amount of ongoing communication and computation. Our algorithmic techniques show interesting connections between periodic scheduling, coloring, and universal prefix free encodings. We develop a coloring-based construction where the period of each node colored with the c is at most 21+log*c ⋅ prodi=0log*c log(i)c (where log(i) means iterating the log function i times). This is achieved via a connection with prefix-free encodings. We prove that this is the best possible for coloring-based solutions. We also show a construction with period at most 2d for a node of degree d.","PeriodicalId":346939,"journal":{"name":"Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124847857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cache-Adaptive Analysis","authors":"M. A. Bender, E. Demaine, Roozbeh Ebrahimi, Jeremy T. Fineman, Rob Johnson, Andrea Lincoln, J. Lynch, Samuel McCauley","doi":"10.1145/2935764.2935798","DOIUrl":"https://doi.org/10.1145/2935764.2935798","url":null,"abstract":"Memory efficiency and locality have substantial impact on the performance of programs, particularly when operating on large data sets. Thus, memory- or I/O-efficient algorithms have received significant attention both in theory and practice. The widespread deployment of multicore machines, however, brings new challenges. Specifically, since the memory (RAM) is shared across multiple processes, the effective memory-size allocated to each process fluctuates over time. This paper presents techniques for designing and analyzing algorithms in a cache-adaptive setting, where the RAM available to the algorithm changes over time. These techniques make analyzing algorithms in the cache-adaptive model almost as easy as in the external memory, or DAM model. Our techniques enable us to analyze a wide variety of algorithms --- Master-Method-style algorithms, Akra-Bazzi-style algorithms, collections of mutually recursive algorithms, and algorithms, such as FFT, that break problems of size N into subproblems of size Theta(Nc). We demonstrate the effectiveness of these techniques by deriving several results: 1. We give a simple recipe for determining whether common divide-and-conquer cache-oblivious algorithms are optimally cache adaptive. 2. We show how to bound an algorithm's non-optimality. We give a tight analysis showing that a class of cache-oblivious algorithms is a logarithmic factor worse than optimal. 3. We show the generality of our techniques by analyzing the cache-oblivious FFT algorithm, which is not covered by the above theorems. Nonetheless, the same general techniques can show that it is at most O(loglog N) away from optimal in the cache adaptive setting, and that this bound is tight. These general theorems give concrete results about several algorithms that could not be analyzed using earlier techniques. For example, our results apply to Fast Fourier Transform, matrix multiplication, Jacobi Multipass Filter, and cache-oblivious dynamic-programming algorithms, such as Longest Common Subsequence and Edit Distance. Our results also give algorithm designers clear guidelines for creating optimally cache-adaptive algorithms.","PeriodicalId":346939,"journal":{"name":"Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127224813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}