Pub Date : 2023-05-31DOI: 10.1007/s00446-023-00451-3
Barun Gorain, Avery Miller, Andrzej Pelc
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.
{"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":null,"pages":null},"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}
Pub Date : 2023-05-15DOI: 10.1007/s00446-023-00447-z
Michal Dory, Mohsen Ghaffari, Saeed Ilchi
Abstract We describe a simple deterministic $$O( varepsilon ^{-1} log Delta )$$ O(ε-1logΔ) round distributed algorithm for $$(2alpha +1)(1 + varepsilon )$$ (2α+1)(1+ε) approximation of minimum weighted dominating set on graphs with arboricity at most $$alpha $$ α . Here $$Delta $$ Δ 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 $$O(alpha ^2)$$ O(α2) approximation in $$O(log n)$$ O(logn) rounds (Lenzen et al. in International symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha log Delta )$$ O(αlogΔ) approximation in $$O(log Delta )$$ O(logΔ) rounds (Lenzen et al. in international symposium on distributed computing, Springer, 2010), a deterministic $$O(alpha )$$ O(α) approximation in $$O(log ^2 Delta )$$ O(log2Δ) rounds (implici
摘要描述了一种简单的确定性$$O( varepsilon ^{-1} log Delta )$$ O (ε - 1 log Δ)轮分布算法，用于求解最大限为$$alpha $$ α的图上的最小加权支配集的$$(2alpha +1)(1 + varepsilon )$$ (2 α + 1) (1 + ε)逼近。其中$$Delta $$ Δ表示最大度。我们还展示了一个下界，通过减少分布式顶点覆盖近似上著名的KMW下界(Kuhn等人在JACM 63:116, 2016)，证明即使在未加权的情况下，这种轮复杂度也几乎是最优的。我们的算法改进了之前的所有结果(仅适用于未加权的图)，包括$$O(log n)$$ O (log n)轮的随机$$O(alpha ^2)$$ O (α 2)近似(Lenzen等人在分布式计算国际研讨会上，Springer, 2010)， $$O(log Delta )$$ O (log Δ)轮的确定性$$O(alpha log Delta )$$ O (α log Δ)近似(Lenzen等人在分布式计算国际研讨会上，Springer, 2010)，在$$O(log ^2 Delta )$$ O (log 2 Δ)轮中的确定性$$O(alpha )$$ O (α)近似(隐含在Bansal等人的Inform Process Lett 122:21 - 24,2017中);进行第17届离散算法研讨会(SODA)， 2006年)，以及$$O(alpha log n)$$ O (α log n)轮的随机$$O(alpha )$$ O (α)近似(Morgan等人在第35届国际分布式计算研讨会上，2021年)。我们还提供了一个随机的$$O(alpha log Delta )$$ O (α log Δ)轮分布算法，该算法将近似因子提高到$$alpha (1+o(1))$$ α (1 + O(1))。如果每个节点被限制进行多项式时间计算，我们的近似因子在一阶上是紧密的，因为它是NP-hard实现$$alpha - 1 - varepsilon $$ α - 1- ε近似(Bansal et al. in Inform Process Lett 122:21- 24,2017)。
{"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":null,"pages":null},"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}
Pub Date : 2022-12-07DOI: 10.1007/s00446-022-00440-y
Armando Castañeda, S. Rajsbaum, M. Raynal
{"title":"Set-Linearizable Implementations from Read/Write Operations: Sets, Fetch &Increment, Stacks and Queues with Multiplicity","authors":"Armando Castañeda, S. Rajsbaum, M. Raynal","doi":"10.1007/s00446-022-00440-y","DOIUrl":"https://doi.org/10.1007/s00446-022-00440-y","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45367692","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}
Pub Date : 2022-08-01DOI: 10.1007/s00446-022-00429-7
W. Cazzola, Francesco Cesarini, Luca Tansini
{"title":"PerformERL: a performance testing framework for erlang","authors":"W. Cazzola, Francesco Cesarini, Luca Tansini","doi":"10.1007/s00446-022-00429-7","DOIUrl":"https://doi.org/10.1007/s00446-022-00429-7","url":null,"abstract":"","PeriodicalId":50569,"journal":{"name":"Distributed Computing","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42509173","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}
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