M. Ghaffari, Erez Kantor, N. Lynch, Calvin C. Newport
We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and contention.We begin by studying upper and lower bounds for this problem in a standard abstract MAC layer model---identifying an interesting dependence between the structure of unreliable links and achievable time complexity. In more detail, given a restriction that devices connected directly by an unreliable link are not too far from each other in the reliable link topology, we can (almost) match the efficiency of the reliable case. For the related restriction, however, that two devices connected by an unreliable link are not too far from each other in geographic distance, we prove a new lower bound that shows that this efficiency is impossible. We then investigate how much extra power must be added to the model to enable a new order of magnitude of efficiency. In more detail, we consider an enhanced abstract MAC layer model and present a new multi-message broadcast algorithm that (under certain natural assumptions) solves the problem in this model faster than any known solutions in an abstract MAC layer setting.
{"title":"Multi-message broadcast with abstract MAC layers and unreliable links","authors":"M. Ghaffari, Erez Kantor, N. Lynch, Calvin C. Newport","doi":"10.1145/2611462.2611492","DOIUrl":"https://doi.org/10.1145/2611462.2611492","url":null,"abstract":"We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and contention.We begin by studying upper and lower bounds for this problem in a standard abstract MAC layer model---identifying an interesting dependence between the structure of unreliable links and achievable time complexity. In more detail, given a restriction that devices connected directly by an unreliable link are not too far from each other in the reliable link topology, we can (almost) match the efficiency of the reliable case. For the related restriction, however, that two devices connected by an unreliable link are not too far from each other in geographic distance, we prove a new lower bound that shows that this efficiency is impossible. We then investigate how much extra power must be added to the model to enable a new order of magnitude of efficiency. In more detail, we consider an enhanced abstract MAC layer model and present a new multi-message broadcast algorithm that (under certain natural assumptions) solves the problem in this model faster than any known solutions in an abstract MAC layer setting.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116038270","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}
In this paper, we study distributed consensus in the radio network setting. We produce new upper and lower bounds for this problem in an abstract MAC layer model that captures the key guarantees provided by most wireless MAC layers. In more detail, we first generalize the well-known impossibility of deterministic consensus with a single crash failure [FLP 1985] from the asynchronous message passing model to our wireless setting. Proceeding under the assumption of no faults, we then investigate the amount of network knowledge required to solve consensus in our model---an important question given that these networks are often deployed in an ad hoc manner. We prove consensus is impossible without unique ids or without knowledge of network size (in multihop topologies). We also prove a lower bound on optimal time complexity. We then match these lower bounds with a pair of new deterministic consensus algorithms---one for single hop topologies and one for multihop topologies---providing a comprehensive characterization of the consensus problem in the wireless setting. From a theoretical perspective, our results shed new insight into the role of network information and the power of MAC layer abstractions in solving distributed consensus. From a practical perspective, given the level of abstraction used by our model, our upper bounds can be easily implemented in real wireless devices on existing MAC layers while preserving their correctness guarantees---facilitating the development of wireless distributed systems.
{"title":"Consensus with an abstract MAC layer","authors":"Calvin C. Newport","doi":"10.1145/2611462.2611479","DOIUrl":"https://doi.org/10.1145/2611462.2611479","url":null,"abstract":"In this paper, we study distributed consensus in the radio network setting. We produce new upper and lower bounds for this problem in an abstract MAC layer model that captures the key guarantees provided by most wireless MAC layers. In more detail, we first generalize the well-known impossibility of deterministic consensus with a single crash failure [FLP 1985] from the asynchronous message passing model to our wireless setting. Proceeding under the assumption of no faults, we then investigate the amount of network knowledge required to solve consensus in our model---an important question given that these networks are often deployed in an ad hoc manner. We prove consensus is impossible without unique ids or without knowledge of network size (in multihop topologies). We also prove a lower bound on optimal time complexity. We then match these lower bounds with a pair of new deterministic consensus algorithms---one for single hop topologies and one for multihop topologies---providing a comprehensive characterization of the consensus problem in the wireless setting. From a theoretical perspective, our results shed new insight into the role of network information and the power of MAC layer abstractions in solving distributed consensus. From a practical perspective, given the level of abstraction used by our model, our upper bounds can be easily implemented in real wireless devices on existing MAC layers while preserving their correctness guarantees---facilitating the development of wireless distributed systems.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133985682","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}
In this paper we present a novel algorithm for concurrent lock-free internal binary search trees (BST) and implement a Set abstract data type (ADT) based on that. We show that in the presented lock-free BST algorithm the amortized step complexity of each set operation - Add, Remove and Contains - is O(H(n) + c), where H(n) is the height of the BST with n number of nodes and c is the contention during the execution. Our algorithm adapts to contention measures according to read-write load. If the situation is read-heavy, the operations avoid helping the concurrent Remove operations during traversal, and adapt to interval contention. However, for the write-heavy situations we let an operation help a concurrent Remove, even though it is not obstructed. In that case, an operation adapts to point contention. It uses single-word compare-and-swap (CAS) operations. We show that our algorithm has improved disjoint-access-parallelism compared to similar existing algorithms. We prove that the presented algorithm is linearizable. To the best of our knowledge, this is the first algorithm for any concurrent tree data-structure in which the modify operations are performed with an additive term of contention measure.
{"title":"Efficient lock-free binary search trees","authors":"Bapi Chatterjee, Nhan Nguyen Dang, P. Tsigas","doi":"10.1145/2611462.2611500","DOIUrl":"https://doi.org/10.1145/2611462.2611500","url":null,"abstract":"In this paper we present a novel algorithm for concurrent lock-free internal binary search trees (BST) and implement a Set abstract data type (ADT) based on that. We show that in the presented lock-free BST algorithm the amortized step complexity of each set operation - Add, Remove and Contains - is O(H(n) + c), where H(n) is the height of the BST with n number of nodes and c is the contention during the execution. Our algorithm adapts to contention measures according to read-write load. If the situation is read-heavy, the operations avoid helping the concurrent Remove operations during traversal, and adapt to interval contention. However, for the write-heavy situations we let an operation help a concurrent Remove, even though it is not obstructed. In that case, an operation adapts to point contention. It uses single-word compare-and-swap (CAS) operations. We show that our algorithm has improved disjoint-access-parallelism compared to similar existing algorithms. We prove that the presented algorithm is linearizable. To the best of our knowledge, this is the first algorithm for any concurrent tree data-structure in which the modify operations are performed with an additive term of contention measure.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126356362","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}
In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let λ be the minimum cut. Our algorithm can compute λ exactly in O((√n+D) poly(λ)) time, where n is the number of nodes (processors) in the network, D is the network diameter, and ~O hides poly log n. By a standard reduction, we can convert this algorithm into a (1+ε)-approximation O((√n+D)/poly(ε))-time algorithm. The latter result improves over the previous (2+ε)-approximation O((√n+D)/poly(ε))-time algorithm of Ghaffari and Kuhn (DISC 2013). Due to the lower bound of ~Ω(√n+D) by Das Sarma et al. (SICOMP 2013), this running time is tight up to a poly log n factor. Our algorithm is an extremely simple combination of Thorup's tree packing theorem [Combinatorica 2007], Kutten and Peleg's tree partitioning algorithm [J. Algorithms 1998], and Karger's dynamic programming [JACM 2000].
{"title":"Brief announcement: almost-tight approximation distributed algorithm for minimum cut","authors":"Danupon Nanongkai","doi":"10.1145/2611462.2611511","DOIUrl":"https://doi.org/10.1145/2611462.2611511","url":null,"abstract":"In this short paper, we present an improved algorithm for approximating the minimum cut on distributed (CONGEST) networks. Let λ be the minimum cut. Our algorithm can compute λ exactly in O((√n+D) poly(λ)) time, where n is the number of nodes (processors) in the network, D is the network diameter, and ~O hides poly log n. By a standard reduction, we can convert this algorithm into a (1+ε)-approximation O((√n+D)/poly(ε))-time algorithm. The latter result improves over the previous (2+ε)-approximation O((√n+D)/poly(ε))-time algorithm of Ghaffari and Kuhn (DISC 2013). Due to the lower bound of ~Ω(√n+D) by Das Sarma et al. (SICOMP 2013), this running time is tight up to a poly log n factor. Our algorithm is an extremely simple combination of Thorup's tree packing theorem [Combinatorica 2007], Kutten and Peleg's tree partitioning algorithm [J. Algorithms 1998], and Karger's dynamic programming [JACM 2000].","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129749022","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}
Signal-strength models of wireless communications capture the gradual fading of signals and the additivity of interference. As such, they are closer to reality than other models. However, nearly all theoretic work in the SINR model depends on the assumption of smooth geometric decay, one that is true in free space but is far off in actual environments. The challenge is to model realistic environments, including walls, obstacles, reflections and anisotropic antennas, without making the models algorithmically impractical or analytically intractable. We present a simple solution that allows the modeling of arbitrary static situations by moving from geometry to arbitrary decay spaces. The complexity of a setting is captured by a metricity parameter ζ that indicates how far the decay space is from satisfying the triangular inequality. All results that hold in the SINR model in general metrics carry over to decay spaces, with the resulting time complexity and approximation depending on ζ in the same way that the original results depends on the path loss term α. For distributed algorithms, that to date have appeared to necessarily depend on the planarity, we indicate how they can be adapted to arbitrary decay spaces at a cost in time complexity that depends on a fading parameter of the decay space. In particular, for decay spaces that are doubling, the parameter is constant-bounded. Finally, we explore the dependence on ζ in the approximability of core problems. In particular, we observe that the capacity maximization problem has exponential upper and lower bounds in terms of ζ in general decay spaces. In Euclidean metrics and related growth-bounded decay spaces, the performance depends on the exact metricity definition, with a polynomial upper bound in terms of ζ, but an exponential lower bound in terms of a variant parameter φ. The upper bound result is the first approximation of a capacity-type SINR problem that is subexponential in α.
{"title":"Beyond geometry: towards fully realistic wireless models","authors":"Marijke H. L. Bodlaender, M. Halldórsson","doi":"10.1145/2611462.2611476","DOIUrl":"https://doi.org/10.1145/2611462.2611476","url":null,"abstract":"Signal-strength models of wireless communications capture the gradual fading of signals and the additivity of interference. As such, they are closer to reality than other models. However, nearly all theoretic work in the SINR model depends on the assumption of smooth geometric decay, one that is true in free space but is far off in actual environments. The challenge is to model realistic environments, including walls, obstacles, reflections and anisotropic antennas, without making the models algorithmically impractical or analytically intractable. We present a simple solution that allows the modeling of arbitrary static situations by moving from geometry to arbitrary decay spaces. The complexity of a setting is captured by a metricity parameter ζ that indicates how far the decay space is from satisfying the triangular inequality. All results that hold in the SINR model in general metrics carry over to decay spaces, with the resulting time complexity and approximation depending on ζ in the same way that the original results depends on the path loss term α. For distributed algorithms, that to date have appeared to necessarily depend on the planarity, we indicate how they can be adapted to arbitrary decay spaces at a cost in time complexity that depends on a fading parameter of the decay space. In particular, for decay spaces that are doubling, the parameter is constant-bounded. Finally, we explore the dependence on ζ in the approximability of core problems. In particular, we observe that the capacity maximization problem has exponential upper and lower bounds in terms of ζ in general decay spaces. In Euclidean metrics and related growth-bounded decay spaces, the performance depends on the exact metricity definition, with a polynomial upper bound in terms of ζ, but an exponential lower bound in terms of a variant parameter φ. The upper bound result is the first approximation of a capacity-type SINR problem that is subexponential in α.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"33 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131501592","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}
Gossip algorithms spread information in distributed networks by nodes repeatedly forwarding information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and message-efficient. A common model for gossip communication is the random phone call model, in which in each synchronous round each node can PUSH or PULL information to or from a random other node. For example, Karp et al. [FOCS 2000] gave algorithms in this model that spread a message to all nodes in Θ(log n) rounds while sending only O(log log n) messages per node on average. They also showed that at least Θ(log n) rounds are necessary in this model and that algorithms achieving this round-complexity need to send ω(1) messages per node on average. Recently, Avin and Elsasser [DISC 2013], studied the random phone call model with the natural and commonly used assumption of direct addressing. Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP address) was learned before. They show that in this setting, one can "break the log n barrier" and achieve a gossip algorithm running in O(√log n) rounds, albeit while using O(√log n) messages per node. In this paper we study the same model and give a simple gossip algorithm which spreads a message in only O(log log n) rounds. We furthermore prove a matching Ω(log log n) lower bound which shows that this running time is best possible. In particular we show that any gossip algorithm takes with high probability at least 0.99 log log n rounds to terminate. Lastly, our algorithm can be tweaked to send only O(1) messages per node on average with only O(log n) bits per message. Our algorithm therefore simultaneously achieves the optimal round-, message-, and bit-complexity for this setting. As all prior gossip algorithms, our algorithm is also robust against failures. In particular, if in the beginning an oblivious adversary fails any F nodes our algorithm still, with high probability, informs all but o(F) surviving nodes.
{"title":"Optimal gossip with direct addressing","authors":"Bernhard Haeupler, D. Malkhi","doi":"10.1145/2611462.2611489","DOIUrl":"https://doi.org/10.1145/2611462.2611489","url":null,"abstract":"Gossip algorithms spread information in distributed networks by nodes repeatedly forwarding information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and message-efficient. A common model for gossip communication is the random phone call model, in which in each synchronous round each node can PUSH or PULL information to or from a random other node. For example, Karp et al. [FOCS 2000] gave algorithms in this model that spread a message to all nodes in Θ(log n) rounds while sending only O(log log n) messages per node on average. They also showed that at least Θ(log n) rounds are necessary in this model and that algorithms achieving this round-complexity need to send ω(1) messages per node on average. Recently, Avin and Elsasser [DISC 2013], studied the random phone call model with the natural and commonly used assumption of direct addressing. Direct addressing allows nodes to directly contact nodes whose ID (e.g., IP address) was learned before. They show that in this setting, one can \"break the log n barrier\" and achieve a gossip algorithm running in O(√log n) rounds, albeit while using O(√log n) messages per node. In this paper we study the same model and give a simple gossip algorithm which spreads a message in only O(log log n) rounds. We furthermore prove a matching Ω(log log n) lower bound which shows that this running time is best possible. In particular we show that any gossip algorithm takes with high probability at least 0.99 log log n rounds to terminate. Lastly, our algorithm can be tweaked to send only O(1) messages per node on average with only O(log n) bits per message. Our algorithm therefore simultaneously achieves the optimal round-, message-, and bit-complexity for this setting. As all prior gossip algorithms, our algorithm is also robust against failures. In particular, if in the beginning an oblivious adversary fails any F nodes our algorithm still, with high probability, informs all but o(F) surviving nodes.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132017262","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}
We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a (7-ε)-approximation of a minimum dominating set on planar graphs, for any positive constant ε. In prior work, the best lower bound on the approximation ratio has been 5-ε; there is also an upper bound of 52.
{"title":"Brief announcement: local approximability of minimum dominating set on planar graphs","authors":"Miikka Hilke, C. Lenzen, J. Suomela","doi":"10.1145/2611462.2611504","DOIUrl":"https://doi.org/10.1145/2611462.2611504","url":null,"abstract":"We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a (7-ε)-approximation of a minimum dominating set on planar graphs, for any positive constant ε. In prior work, the best lower bound on the approximation ratio has been 5-ε; there is also an upper bound of 52.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115049551","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}
A fundamental problem in distributed network algorithms is to manage congestion and obtain information flow matching the graph's connectivity. In this paper, we present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. These decompositions allow us to achieve a flow with size close to the connectivity by parallelizing it along the trees. More specifically, our distributed decomposition algorithms are as follows: - A decomposition of each undirected graph with vertex-connectivity k into (fractionally) vertex-disjoint weighted dominating trees with total weight Ω(k/log n), in ~O(D+√n) rounds. - A decomposition of each undirected graph with edge-connectivity λ into (fractionally) edge-disjoint weighted spanning trees with total weight ⌈λ-1/2⌉(1-ε), in ~{O}(D+√nλ) rounds. We also show round complexity lower bounds of ~](D+√n/k) and ~Ω(D+√n/λ) for the above two decompositions, using techniques of [Das Sarma et al., STOC'11]. Moreover, our vertex-connectivity decomposition extends to centralized algorithms and improves the time complexity of [Censor-Hillel et al., SODA'14] from O(n3) to near-optimal ~O(m). Additional implications of our results are: a near-linear time centralized approximation of vertex connectivity which can be seen as a step towards a conjecture of Aho, Hopcroft and Ullman), the first distributed approximating of vertex connectivity, and distributed algorithms with near-optimal competitiveness for oblivious broadcast routing.
分布式网络算法的一个基本问题是管理拥塞并获得与图的连通性相匹配的信息流。在本文中，我们提出了一种时间高效的分布式算法，用于将具有大边或大顶点连接的图分别分解为多个生成树或支配树。这些分解允许我们通过沿着树并行化来实现与连接性接近的流。更具体地说，我们的分布式分解算法如下:-将每个具有顶点连通性k的无向图分解为(部分地)顶点不相交的加权支配树，总权重为Ω(k/log n)，在~O(D+√n)轮中。-将每个具有边连性λ的无向图分解为(分数地)总权为(λ-1/2) (1-ε)的边不相交加权生成树，以~{O}(D+√nλ)轮进行分解。我们还使用[Das Sarma et al.， STOC'11]的技术，展示了上述两种分解的圆复杂度下界~](D+√n/k)和~Ω(D+√n/λ)。此外，我们的顶点连通性分解扩展到集中式算法，并将[Censor-Hillel et al.， SODA'14]的时间复杂度从O(n3)提高到接近最优的~O(m)。我们的结果的其他含义是:顶点连通性的近线性时间集中近似(可以看作是向Aho, Hopcroft和Ullman猜想迈出的一步)，顶点连通性的第一个分布式近似，以及具有近最优竞争力的分布式算法对于遗忘广播路由。
{"title":"Distributed connectivity decomposition","authors":"K. Censor-Hillel, M. Ghaffari, F. Kuhn","doi":"10.1145/2611462.2611491","DOIUrl":"https://doi.org/10.1145/2611462.2611491","url":null,"abstract":"A fundamental problem in distributed network algorithms is to manage congestion and obtain information flow matching the graph's connectivity. In this paper, we present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. These decompositions allow us to achieve a flow with size close to the connectivity by parallelizing it along the trees. More specifically, our distributed decomposition algorithms are as follows: - A decomposition of each undirected graph with vertex-connectivity k into (fractionally) vertex-disjoint weighted dominating trees with total weight Ω(k/log n), in ~O(D+√n) rounds. - A decomposition of each undirected graph with edge-connectivity λ into (fractionally) edge-disjoint weighted spanning trees with total weight ⌈λ-1/2⌉(1-ε), in ~{O}(D+√nλ) rounds. We also show round complexity lower bounds of ~](D+√n/k) and ~Ω(D+√n/λ) for the above two decompositions, using techniques of [Das Sarma et al., STOC'11]. Moreover, our vertex-connectivity decomposition extends to centralized algorithms and improves the time complexity of [Censor-Hillel et al., SODA'14] from O(n3) to near-optimal ~O(m). Additional implications of our results are: a near-linear time centralized approximation of vertex connectivity which can be seen as a step towards a conjecture of Aho, Hopcroft and Ullman), the first distributed approximating of vertex connectivity, and distributed algorithms with near-optimal competitiveness for oblivious broadcast routing.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115941165","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}
We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be solvable in M. When applied to the wait-free model, our conditions result in the celebrated Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate the utility of our characterization, we consider a task that has been shown earlier to admit only a very complex t-resilient solution. In contrast, our generalized computability theorem confirms its t-resilient solvability in a straightforward manner.
{"title":"A generalized asynchronous computability theorem","authors":"E. Gafni, P. Kuznetsov, Ciprian Manolescu","doi":"10.1145/2611462.2611477","DOIUrl":"https://doi.org/10.1145/2611462.2611477","url":null,"abstract":"We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be solvable in M. When applied to the wait-free model, our conditions result in the celebrated Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate the utility of our characterization, we consider a task that has been shown earlier to admit only a very complex t-resilient solution. In contrast, our generalized computability theorem confirms its t-resilient solvability in a straightforward manner.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130490258","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}
We advocate rigorous system design as a coherent and accountable model-based process leading from requirements to implementations. We present the state of the art in system design, discuss its current limitations, and identify possible avenues for overcoming them. A rigorous system design flow [3] is defined as a formal accountable and iterative process composed of steps, and based on four principles: (1) separation of concerns; (2) component-based construction; (3) semantic coherency; and (4) correctness-by-construction. We show that the combined application of these principles allows the definition of rigorous design flows clearly identifying where human intervention and ingenuity are needed to resolve design choices, as well as activities that can be supported by tools to automate tedious and error-prone tasks. An implementable system model is progressively derived by source-to-source automated transformations in a single host component-based language rooted in well-defined semantics. Using a single modeling language throughout the design flow enforces semantic coherency. Correct-by-construction techniques allow well-known limitations of a posteriori verification to be overcome and ensure accountability. It is possible to explain, at each design step, which among the requirements are satisfied and which may not be satisfied. The presented view has been amply implemented in the BIP (Behavior, Interaction, Priority) component framework and substantiated by numerous experimental results showing both its relevance and feasibility [1]. We show in particular, how distributed implementations can be generated from BIP models with multiparty interactions by application of correct-by-construction transformations [2]. We conclude with a discussion advocating a system-centric vision for computing, identifying possible links with other disciplines, and emphasizing centrality of system design.
{"title":"Rigorous system design","authors":"J. Sifakis","doi":"10.1145/2611462.2611517","DOIUrl":"https://doi.org/10.1145/2611462.2611517","url":null,"abstract":"We advocate rigorous system design as a coherent and accountable model-based process leading from requirements to implementations. We present the state of the art in system design, discuss its current limitations, and identify possible avenues for overcoming them. A rigorous system design flow [3] is defined as a formal accountable and iterative process composed of steps, and based on four principles: (1) separation of concerns; (2) component-based construction; (3) semantic coherency; and (4) correctness-by-construction. We show that the combined application of these principles allows the definition of rigorous design flows clearly identifying where human intervention and ingenuity are needed to resolve design choices, as well as activities that can be supported by tools to automate tedious and error-prone tasks. An implementable system model is progressively derived by source-to-source automated transformations in a single host component-based language rooted in well-defined semantics. Using a single modeling language throughout the design flow enforces semantic coherency. Correct-by-construction techniques allow well-known limitations of a posteriori verification to be overcome and ensure accountability. It is possible to explain, at each design step, which among the requirements are satisfied and which may not be satisfied. The presented view has been amply implemented in the BIP (Behavior, Interaction, Priority) component framework and substantiated by numerous experimental results showing both its relevance and feasibility [1]. We show in particular, how distributed implementations can be generated from BIP models with multiparty interactions by application of correct-by-construction transformations [2]. We conclude with a discussion advocating a system-centric vision for computing, identifying possible links with other disciplines, and emphasizing centrality of system design.","PeriodicalId":186800,"journal":{"name":"Proceedings of the 2014 ACM symposium on Principles of distributed computing","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122282191","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}
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