Distributed Computing最新文献_第3页

Correction to: Distributed computations in fully-defective networks 修正:全缺陷网络中的分布式计算

4区计算机科学

Distributed Computing Pub Date : 2023-09-30 DOI: 10.1007/s00446-023-00457-x

Keren Censor-Hillel, Shir Cohen, Ran Gelles, Gal Sela

引用次数: 1

Almost universally optimal distributed Laplacian solvers via low-congestion shortcuts 通过低拥塞捷径的几乎普遍最优的分布式拉普拉斯解

4区计算机科学

Distributed Computing Pub Date : 2023-07-31 DOI: 10.1007/s00446-023-00454-0

Ioannis Anagnostides, Christoph Lenzen, Bernhard Haeupler, Goran Zuzic, Themis Gouleakis

{"title":"Almost universally optimal distributed Laplacian solvers via low-congestion shortcuts","authors":"Ioannis Anagnostides, Christoph Lenzen, Bernhard Haeupler, Goran Zuzic, Themis Gouleakis","doi":"10.1007/s00446-023-00454-0","DOIUrl":"https://doi.org/10.1007/s00446-023-00454-0","url":null,"abstract":"Abstract In this paper, we refine the (almost) existentially optimal distributed Laplacian solver of Forster, Goranci, Liu, Peng, Sun, and Ye (FOCS ‘21) into an (almost) universally optimal distributed Laplacian solver. Specifically, when the topology is known (i.e., the Supported-CONGEST model), we show that any Laplacian system on an n -node graph with shortcut quality $$textrm{SQ}(G)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mtext>SQ</mml:mtext> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> can be solved after $$n^{o(1)} text {SQ}(G) log (1/epsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi>o</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mtext>SQ</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>log</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>ϵ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> rounds, where $$epsilon >0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is the required accuracy. This almost matches our lower bound that guarantees that any correct algorithm on G requires $$widetilde{Omega }(textrm{SQ}(G))$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mover> <mml:mi>Ω</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mrow> <mml:mo>(</mml:mo> <mml:mtext>SQ</mml:mtext> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> rounds, even for a crude solution with $$epsilon le 1/2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ϵ</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Several important implications hold in the unknown-topology (i.e., standard CONGEST) case: for excluded-minor graphs we get an almost universally optimal algorithm that terminates in $$D cdot n^{o(1)} log (1/epsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>·</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi>o</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>log</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mi>ϵ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> rounds, where D is the hop-diameter of the network; as well as $$n^{o(1)} log (1/epsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mi>o</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> <mml:mo>log</mml:mo> <mml:mrow> <mml:mo>(</m","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135208696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Special issue on PODC 2021 and DISC 2021 PODC 2021和DISC 2021特刊

IF 1.3 4区计算机科学

Distributed Computing Pub Date : 2023-07-29 DOI: 10.1007/s00446-023-00456-y

H. Attiya

引用次数: 0

Near-optimal distributed computation of small vertex cuts 小顶点切割的近最优分布计算

IF 1.3 4区计算机科学

Distributed Computing Pub Date : 2023-07-14 DOI: 10.1007/s00446-023-00455-z

Merav Parter, Asaf Petruschka

{"title":"Near-optimal distributed computation of small vertex cuts","authors":"Merav Parter, Asaf Petruschka","doi":"10.1007/s00446-023-00455-z","DOIUrl":"https://doi.org/10.1007/s00446-023-00455-z","url":null,"abstract":"We present near-optimal algorithms for detecting small vertex cuts in the ({textsf{CONGEST}}) model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete, especially in the distributed setting. To this date, all distributed algorithms for detecting cut vertices suffer from an inherent dependency in the maximum degree of the graph, (Delta ). Hence, in particular, there is no truly sub-linear time algorithm for this problem, not even for detecting a single cut vertex. We take a new algorithmic approach for vertex connectivity which allows us to bypass the existing (Delta ) barrier. As a warm-up to our approach, we show a simple (widetilde{O}(D))-round randomized algorithm for computing all cut vertices in a D-diameter n-vertex graph. This improves upon the (O(D+Delta /log n))-round algorithm of [Pritchard and Thurimella, ICALP 2008]. Our key technical contribution is an (widetilde{O}(D))-round randomized algorithm for computing all cut pairs in the graph, improving upon the state-of-the-art (O(Delta cdot D)^4)-round algorithm by [Parter, DISC ’19]. Note that even for the considerably simpler setting of edge cuts, currently (widetilde{O}(D))-round algorithms are known only for detecting pairs of cut edges. Our approach is based on employing the well-known linear graph sketching technique [Ahn, Guha and McGregor, SODA 2012] along with the heavy-light tree decomposition of [Sleator and Tarjan, STOC 1981]. Combining this with a careful characterization of the survivable subgraphs, allows us to determine the connectivity of (G {setminus } {x,y}) for every pair (x,y in V), using (widetilde{O}(D))-rounds. We believe that the tools provided in this paper are useful for omitting the (Delta )-dependency even for larger cut values.","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Node and edge averaged complexities of local graph problems 局部图问题的节点和边平均复杂度

IF 1.3 4区计算机科学

Distributed Computing Pub Date : 2023-07-05 DOI: 10.1007/s00446-023-00453-1

Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Dennis Olivetti

{"title":"Node and edge averaged complexities of local graph problems","authors":"Alkida Balliu, Mohsen Ghaffari, Fabian Kuhn, Dennis Olivetti","doi":"10.1007/s00446-023-00453-1","DOIUrl":"https://doi.org/10.1007/s00446-023-00453-1","url":null,"abstract":"We continue the recently started line of work on the distributed node-averaged complexity of distributed graph algorithms. The node-averaged complexity of a distributed algorithm running on a graph (G=(V,E)) is the average over the times at which the nodes V of G finish their computation and commit to their outputs. We study the node-averaged complexity for some of the central distributed symmetry breaking problems and provide the following results (among others). As our main result, we show that the randomized node-averaged complexity of computing a maximal independent set (MIS) in n-node graphs of maximum degree (Delta ) is at least (Omega big (min big {frac{log Delta }{log log Delta },sqrt{frac{log n}{log log n}}big }big )). This bound is obtained by a novel adaptation of the well-known lower bound by Kuhn, Moscibroda, and Wattenhofer [JACM’16]. As a side result, we obtain that the worst-case randomized round complexity for computing an MIS in trees is also (Omega big (min big {frac{log Delta }{log log Delta },sqrt{frac{log n}{log log n}}big }big ))—this essentially answers open problem 11.15 in the book by Barenboim and Elkin and resolves the complexity of MIS on trees up to an (O(sqrt{log log n})) factor. We also show that, perhaps surprisingly, a minimal relaxation of MIS, which is the same as (2, 1)-ruling set, to the (2, 2)-ruling set problem drops the randomized node-averaged complexity to O(1). For maximal matching, we show that while the randomized node-averaged complexity is (Omega big (min big {frac{log Delta }{log log Delta },sqrt{frac{log n}{log log n}}big }big )), the randomized edge-averaged complexity is O(1). Further, we show that the deterministic edge-averaged complexity of maximal matching is (O(log ^2Delta + log ^* n)) and the deterministic node-averaged complexity of maximal matching is (O(log ^3Delta + log ^* n)). Finally, we consider the problem of computing a sinkless orientation of a graph. The deterministic worst-case complexity of the problem is known to be (Theta (log n)), even on bounded-degree graphs. We show that the problem can be solved deterministically with node-averaged complexity (O(log ^* n)), while keeping the worst-case complexity in (O(log n)).\u0000","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"20 11","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Distributed computations in fully-defective networks 全缺陷网络中的分布式计算

4区计算机科学

Distributed Computing Pub Date : 2023-06-19 DOI: 10.1007/s00446-023-00452-2

Keren Censor-Hillel, Shir Cohen, Ran Gelles, Gal Sela

引用次数: 0

Four shades of deterministic leader election in anonymous networks 匿名网络中确定性领导人选举的四种阴影

4区计算机科学

Distributed Computing Pub Date : 2023-05-31 DOI: 10.1007/s00446-023-00451-3

Barun Gorain, Avery Miller, Andrzej Pelc

{"title":"Four shades of deterministic leader election in anonymous networks","authors":"Barun Gorain, Avery Miller, Andrzej Pelc","doi":"10.1007/s00446-023-00451-3","DOIUrl":"https://doi.org/10.1007/s00446-023-00451-3","url":null,"abstract":"Leader election is one of the fundamental problems in distributed computing: a single node, called the leader, must be specified. This task can be formulated either in a weak way, where one node outputs leader and all other nodes output non-leader, or in a strong way, where all nodes must also learn which node is the leader. If the nodes of the network have distinct identifiers, then such an agreement means that all nodes have to output the identifier of the elected leader. For anonymous networks, the strong version of leader election requires that all nodes must be able to find a path to the leader, as this is the only way to identify it. In this paper, we study variants of deterministic leader election in arbitrary anonymous networks. Leader election is impossible in some anonymous networks, regardless of the allocated amount of time, even if nodes know the entire map of the network. This is due to possible symmetries in the network. However, even in networks in which it is possible to elect a leader knowing the map, the task may be still impossible without any initial knowledge, regardless of the allocated time. On the other hand, for any network in which leader election (weak or strong) is possible knowing the map, there is a minimum time, called the election index, in which this can be done. We consider four formulations of leader election discussed in the literature in the context of anonymous networks: one is the weak formulation, and the three others specify three different ways of finding the path to the leader in the strong formulation. Our aim is to compare the amount of initial information needed to accomplish each of these “four shades” of leader election in minimum time. Following the framework of algorithms with advice, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire network. The length of this string is called the size of advice. We show that the size of advice required to accomplish leader election in the weak formulation in minimum time is exponentially smaller than that needed for any of the strong formulations. Thus, if the required amount of advice is used as a measure of the difficulty of the task, the weakest version of leader election in minimum time is drastically easier than any version of the strong formulation in minimum time.","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135195866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Near-optimal distributed dominating set in bounded arboricity graphs 有界树性图的近最优分布支配集

4区计算机科学

Distributed Computing Pub Date : 2023-05-15 DOI: 10.1007/s00446-023-00447-z

Michal Dory, Mohsen Ghaffari, Saeed Ilchi

{"title":"Near-optimal distributed dominating set in bounded arboricity graphs","authors":"Michal Dory, Mohsen Ghaffari, Saeed Ilchi","doi":"10.1007/s00446-023-00447-z","DOIUrl":"https://doi.org/10.1007/s00446-023-00447-z","url":null,"abstract":"Abstract We describe a simple deterministic $$O( varepsilon ^{-1} log Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mo>log</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> round distributed algorithm for $$(2alpha +1)(1 + varepsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mi>α</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> approximation of minimum weighted dominating set on graphs with arboricity at most $$alpha $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>α</mml:mi> </mml:math> . Here $$Delta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>Δ</mml:mi> </mml:math> denotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation (Kuhn et al. in JACM 63:116, 2016). Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized $$O(alpha ^2)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>α</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> approximation in $$O(log n)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mo>log</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> rounds (Lenzen et al. in International symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha log Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>log</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> approximation in $$O(log Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mo>log</mml:mo> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> rounds (Lenzen et al. in international symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> approximation in $$O(log ^2 Delta )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mo>log</mml:mo> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>Δ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> rounds (implici","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135140602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Termination of amnesiac flooding 终止失忆症洪水

IF 1.3 4区计算机科学

Distributed Computing Pub Date : 2023-05-01 DOI: 10.1007/s00446-023-00448-y

W. Hussak, Amitabh Trehan

引用次数: 0

Special issue on DISC 2019 DISC 2019特刊

IF 1.3 4区计算机科学

Distributed Computing Pub Date : 2023-02-27 DOI: 10.1007/s00446-023-00445-1

H. Attiya

引用次数: 0