N. Linial. Distributive Graph Algorithms - Global Solutions from Local Data. In Proc. of the 28th Ann. IEEE Symp. on Foundations of Computer Science, pp. 331-335, 1987. 14  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a Minimum Spanning Tree (MST) Note that, informally speaking, MST can be thought of as a more global problem, as opposed to the k Dominating Set problem which is more local in nature. We now present a formal notion of what we mean by a fast algorithm, which applies to both. Linial [Li] proved lower bounds on the time complexity of distributed algorithms, even when assuming a very strong computational model (not assumed here) where messages can be of arbitrary length. Yet sending a message from a node to a distance d still takes time d in this model. Thus the lower bounds of ....

....[Li] proved lower bounds on the time complexity of distributed algorithms, even when assuming a very strong computational model (not assumed here) where messages can be of arbitrary length. Yet sending a message from a node to a distance d still takes time d in this model. Thus the lower bounds of [Li] actually correspond only to the radius (around each node) from which information must be fetched in order to solve a given problem P . Let this radius be R(P ) for a given problem P . We term an algorithm for P neighborhood optimal if its complexity is O(R(P ) We use the word fast with ....

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N. Linial, Distributive graph algorithms - global solutions from local data, Proc. 28th IEEE Symp. on Foundations of Computer Science, October 1987, pp. 331{ 335.

....Processors in a distributed environment must make decisions based only on local data, thus fast distributed algorithms must often do without global information about the system as a whole. This is exactly why computing many target functions in distributed models quickly is provably hard [13]. However, quite surprisingly, some of the most interesting global optimization problems can be very closely approximated based only on local information and a modest amount of local communication. Our work is motivated by the application of developing ow control policies which must achieve ....

N. Linial. Distributive Graph Algorithms - Global Solutions from Local Data. In Proc. of the 28th Ann. IEEE Symp. on Foundations of Computer Science, pp. 331-335, 1987.

....in [22] and uses the same scheme as in [20] and [13] However, unlike these works, the algorithm minimizes the radius of influence each operation causes, that is, decreases the sensitivity of the implementation and increases parallelism. Two works are related to our lower bounds. Linial, in [16], proves that in a message passing model a maximal independent set in an n ring can not be found in less than Omega Gamma log n) rounds. We use this proof to prove our first lower bound. Valois, in [23] proves that n distinct states in the shared memory are required if n processors apply a ....

....otherwise, it exists as a non member. Following, we show that in any algorithm for the maximal independent set problem which uses only unary operations, there is an execution in which any processor performs at least Omega Gammast log n) steps. The proof is similar to Linial s lower bound proof [16]. However, while Linial s result regards the message passing model, and prove that the number of rounds required to solve the MIS problem is Omega Gamma 25 n) our result regards the shared memory model and proves a smaller bound. 39 Linial s basic observation in a message passing model is that ....

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N. Linial, "Distributive Graph Algorithms---Global Solutions from Local Data", Foundations Of Computer Science 1987, pp. 331--335, 1987.

....computed distributedly on a network of communicating elements, distributed algorithms were also designed for this problem. In the case of bounded degree networks, an efficient distributed algorithm was proposed in [12] which finds a MIS in O(log n) time. This result was proved to be optimal in [16]. However, if the network degree is unbounded, the problem is again very difficult to solve deterministically, and the best known deterministic distributed algorithm is intricate and takes O(n o(1) time [3] Parallel models of computation On the other hand, from the parallel systems ....

Nathan Linial. Distributive graph algorithms -- global solutions from local data. In 28th FOCS, volume 28, pages 331--335, Oct 1987.

....the design of distributed algorithms for static and dynamic networks has rapidly developed in recent years, the study of lower bounds on the complexity of such protocols was lagging behind. Moreover, most of the existing lower bounds for distributed computing are for computations on a ring network [1, 2, 3, 4, 5, 6]. True, in static networks it is often the case that the ring lower bound is close or is easily extended to a lower bound on general networks (e.g. leader election lower bounds) In dynamic networks however, the situation is different and a big gap usually exists there between the lower bound on a ....

N. Linial. Distributive graph algorithms - global solutions from local data. In Proc. of the 28th IEEE Ann. Symp. on Foundation of Computer Science, pages 331--335, October 1987.

....we study self stabilizing protocols for uniform unidirectional rings. Many basic issues in distributed computing arise from restricted communication (locality) faults and uniformity. In particular, rings are the basic ground for investigating the fundamentals of symmetry in distributed computing ([6, 21, 17, 31, 15, 11, 26, 22]) to mention just a few examples) From a practical point of view, various flavors of token rings (see [33] are popular examples of unidirectional ring structures. Our network model is motivated by the FDDI (Fiber Distributed Data Interface) a high performance 100 Mbps fiber optic token ring ....

N. Linial, Distributive Graph Algorithms-- Global Solutions from Local Data. In Proc. of the 28th IEEE Ann. Symp. on Foundation of Computer Science, October 1987, 331--335.

....context of studying the role of locality in distributed computing. Various problems were shown to be essentially local, and hence amenable to a localized algorithm with very fast (e.g. polylogarithmic) running times. Notable examples include computing maximal independent sets and graph coloring [GPS, L, AGLP, PS2]. Locality based techniques were developed for reducing communication and time complexities also for other problems, whose local nature is less apparent [AP1, AP2, AKP] In contrast, we are interested here with problems that are essentially global, i.e. ones that do not admit localized solutions, ....

....ff [A2] enables an asynchronous network to run any protocol that was designed for synchronous networks, with the same time complexity, at the cost of some increase in the message complexity. Still, we shall not adopt the extreme model employed in previous studies of locality issues (cf. [L]) in which messages of arbitrary size are allowed to be transmitted in a single time unit, since in this model, the refined distinctions we focus on here disappear. Clearly, if unbounded size messages are allowed, then the problem can be trivially solved in time O(Diam(G) by collecting the ....

N. Linial, Distributive graph algorithms - global solutions from local data, Proc. 28th IEEE Symp. on Foundations of Computer Science, pp. 331--335, October 1987.

....1 Introduction Processors in a distributed environment make decisions based only on local data. Therefore, fast distributed algorithms must do without global information about the system as a whole. This is exactly why computing many target functions in distributed models quickly is provably hard [L87]. However, quite surprisingly, some of the most interesting global optimization problems can be very closely approximated based only on local information. We study the problem of developing flow control policies with global objective functions. Flow control is the mechanism by which routers of a ....

N. Linial. Distributive Graph Algorithms - Global Solutions from Local Data. In Proc. of the 28th Ann. IEEE Symp. on Foundations of Computer Science, pp. 331-335, 1987.

....we study self stabilizing protocols for uniform unidirectional rings. Many basic issues in distributed computing arise from restricted communication (locality) faults and uniformity. In particular, rings are the basic ground for investigating the fundamentals of symmetry in distributed computing ([Ang80, IR81, FL84, P82, DKR82, CV86, Li88, It90]) to mention just a few examples) From a practical point of view, various flavors of token rings (see [Tan89] are popular examples of unidirectional ring structures. Our network model is motivated by the FDDI (Fiber Distributed Data Interface) a high performance 100 Mbps fiber optic token ring ....

N. Linial, Distributive Graph Algorithms-- Global Solutions from Local Data. In Proc. of the 28th IEEE Ann. Symp. on Foundation of Computer Science, October 1987, 331--335.

....tries to write its id in m i and m next i . Processor p i load links m i and m next i ; if they are both it tries to 2SC its id, i, atomically to two memory words, m i and m next i . If it succeeds, it exists as a member; otherwise, it exists as a non member. The lower bound result of Linial [15] can be modified to show that in a shared memory model, where only LL and unary SC are allowed, then for any algorithm for the maximal independence problem there is an execution in which any processor performs at least Omega Gammaeas log n) steps. Linial s basic observation in a message ....

....B x;n . To see this, suppose c maps (v i ; v 2x i ) and (y; v i ; v 2x i Gamma1 ) to the same color. Then the algorithm for 3 coloring of a ring fails if the the labeling happens to contain the segment (y; v i ; v 2x i Gamma1 ; v 2x i ) Finally, we use the fact, proved in [15], that (B x;n ) Omega Gamma364 (2x) n) Therefore, for (B x;n ) to be at most 3, we must have x = Omega Gamma465 n) that is, t = Omega Gamma332 log (n) 7 Conclusions This paper defines the sensitivity of an implementation of one object from other objects. Sensitivity is ....

N. Linial, "Distributive Graph Algorithms--- Global Solutions from Local Data," FOCS 1987, 1987, pp. 331--335.

....again message complexity rises sky high. The network diameter serves as a time lower bound for all tasks that require coordination between all nodes (including every task that requires consensus in the output) because no information can be communicated across the network in o(D) time. Linial [15] gives examples of tasks (Maximal Independent Set, Colouring) that can be solved by local computations, i.e. in sub diameter time, and Litovsky et al. 16] have further investigated the power of local computations. 1.3 Examples of Distributed Architectures in AI Distribution may be driven by ....

Nathan Linial. Distributive graph algorithms: Global solutions from local data. In Foundations of Computer Science, pages 331--335. IEEE, 1987.

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N. Linial. Distributive Graph Algorithms - Global Solutions from Local Data. In Proc. of the 28th Ann. IEEE Symp. on Foundations of Computer Science, pp. 331-335, 1987. 14

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. N. Linial. Distributive graph algorithms --- global solutions from local data. Proc. 1987 IEEE Symposium on Foundations of Computer Science, 331-336(1987).

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. N. Linial. Distributive graph algorithms --- global solutions from local data, Proc. 1987.

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. N. Linial. Distributive graph algorithms --- global solutions from local data, Proc. 1987.

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N. Linial. Distributive Graph Algorithms - Global Solutions from Local Data. In Proc. of the 28th Ann. IEEE Symp. on Foundations of Computer Science, pp. 331-335, 1987.

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