{"title":"Massively Parallel Algorithms for Finding Well-Connected Components in Sparse Graphs","authors":"Sepehr Assadi, Xiaorui Sun, Omri Weinstein","doi":"10.1145/3293611.3331596","DOIUrl":"https://doi.org/10.1145/3293611.3331596","url":null,"abstract":"Massively parallel computation (MPC) algorithms for graph problems have witnessed a resurgence of interest in recent years. Despite major progress for numerous graph problems however, the complexity of the sparse graph connectivity problem in this model has remained elusive: While classical logarithmic-round PRAM algorithms for finding connected components in any n-vertex graph have been known for more than three decades (and imply the same bounds for MPC model), no o(log n)-round MPC algorithms are known for this task with truly sublinear in n memory per machine (which is the only interesting regime for sparse graphs with O(n) edges). It is conjectured that an o(log n)-round algorithm for connectivity on general sparse graphs with n1-Ω (1) per-machine memory may not exist, a conjecture that also forms the basis for multiple conditional hardness results on the round complexity of other problems in the MPC model. We take an opportunistic approach towards the sparse graph connectivity problem by designing an algorithm with improved performance in terms of the connectivity structure of the input graph. Formally, we design an MPC algorithm that finds all connected components with spectral gap at least λ in a graph in O(log log n + log(1/λ)) MPC rounds and nδ memory per machine for any constant δ ∈ (0,1). While this algorithm still requires Θ(log n) rounds in the worst-case, it achieves an exponential round reduction on \"well-connected'' components with λ ≥ 1/polylog(n) using only nδ memory per machine and ł(n) total memory, and still operates in o(log n)l rounds even when λ = 1/no(1). En-route to our main result, we design a new distributed data structure for performing independent random walks from all vertices simultaneously, as well as a new leader-election algorithm with exponentially faster round complexity on random graphs.","PeriodicalId":153766,"journal":{"name":"Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126003865","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":"Partially Replicated Causally Consistent Shared Memory: Lower Bounds and An Algorithm","authors":"Zhuolun Xiang, N. Vaidya","doi":"10.1145/3293611.3331600","DOIUrl":"https://doi.org/10.1145/3293611.3331600","url":null,"abstract":"The focus of this paper is on causal consistency in a partially replicated distributed shared memory (DSM) system that provides the abstraction of shared read/write registers. Maintaining causal consistency in distributed shared memory systems has received significant attention in the past, mostly on full replication wherein each replica stores a copy of all the registers in the shared memory. To ensure causal consistency, all causally preceding updates must be performed before an update is performed at any given replica. Therefore, some mechanism for tracking causal dependencies is required, such as vector timestamps with the number of vector elements being equal to the number of replicas in the context of full replication. In this paper, we investigate causal consistency in partially replicated systems, wherein each replica may store only a subset of the shared registers. Building on the past work, this paper makes three key contributions: present a necessary condition on the metadata (which we refer as a timestamp) that must be maintained by each replica to be able to track causality accurately. The necessary condition identifies a set of directed edges in a share graph that a replica's timestamp must keep track of. We present an algorithm for achieving causal consistency using a timestamp that matches the above necessary condition, thus showing that the condition is necessary and sufficient. We define a measurement of timestamp space size and present a lower bound (in bits) on the size of the timestamps. The lower bound matches our algorithm in several special cases.","PeriodicalId":153766,"journal":{"name":"Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127239198","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":"Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing","authors":"Chryssis Georgiou, P. Spirakis","doi":"10.1145/3293611","DOIUrl":"https://doi.org/10.1145/3293611","url":null,"abstract":"It is our great pleasure to welcome you to the 2015 ACM Symposium on Principles of Distributed Computing -- PODC'15. This year's symposium continues its tradition of being the premier forum for presentation of research on all aspects of distributed computing, including the theory, design, implementation and application of distributed algorithms, systems and networks. During the years, PODC has been the stage where many landmark results have been presented that have increased our understanding of this exciting and fundamental research endeavor. In the best tradition of theoretical discovery, the insights that have been provided have not only elucidated fundamental conceptual issues but also found their way into the real world of systems and applications. \u0000 \u0000The call for paper attracted 191 regular submissions and 20 brief announcements. The Program Committee accepted 45 papers and 10 brief announcements that cover a wide variety of topics. Every submitted paper was read and evaluated by at least three reviewers. The final decisions regarding acceptance or rejection of each paper were made through teleconference and electronic Program Committee discussions held during April 2015. Revised and expanded versions of a few selected papers will be considered for publication in a special issue of the journal Distributed Computing and in the Journal of the ACM. \u0000 \u0000The Program Committee has selected the paper \"Deterministic (Delta+1) Coloring in Sublinear (in Delta) Time, in Static, Dynamic and Faulty Networks\" by Leonid Barenboim for this year's Best Paper Award. In addition, the Program Committee selected the paper \"Near-Optimal Scheduling of Distributed Algorithms\" by Mohsen Ghaffari for the Best Student Paper Award. Three keynote talks will be given by Christos Papadimitriou, Moti Yung and Friedhelm Meyer auf der Heide. \u0000 \u0000The 2015 Edsger W. Dijkstra Prize in Distributed Computing is given jointly to the papers \"Another Advantage of Free Choice: Completely Asynchronous Agreement Protocols\", by Michael Ben-Or, published in Proceedings of the 2nd ACM Symposium on Principles of Distributed Computing (1983) and \"Randomized Byzantine Generals\", by Michael O. Rabin, published in Proceedings of 24th IEEE Annual Symposium on Foundations of Computer Science (1983). It will be presented at the International Symposium on Distributed Computing (DISC'15). The 2015 Principles of Distributed Computing Doctoral Dissertation Award is given to \"Efficient Network Utilization in Locality-Sensitive Distributed Algorithms\", by Leonid Barenboim, supervised by Professor Michael Elkin at Ben Gurion University. It will be presented here. \u0000 \u0000Finally, this year we will celebrate the 60th birthday of Alexander A. Shvartsman.","PeriodicalId":153766,"journal":{"name":"Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126784919","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}