S. Cheung, "Efficient Quorumcast Routing Algorithms," Proceedings of IEEE Infocom'94, Toronto, Canada, June 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....ff deadlock timeout is used, then the operation is restarted. Majority quorum consensus has been adopted to collect quorums from the top cluster for synchronous operations, although any other policy could have been used. Several quorum collection policies are discussed in the literature [AR91, CK94, GL92] Two straightforward solutions are to poll nodes serially one at a time until q nodes have responded (where q is the quorum size) or to send the request in parallel to all nodes. The first solution experiences excessive delay while the second incurs high traffic and causes congestion. ....

....then contacting more if report failures occur or to send to q ffl nodes in parallel. Since the extra nodes to send to are to account for failures, and since in our model it is assumed that failures do not occur, the adopted policy is to send the request to exactly q nodes in parallel. In [CK94] several heuristics have been presented to access q nodes out of m with minimum costs given the topology and communication cost between each pair of nodes. However, since nodes in the top cluster are assumed to be fully connected with the same link speeds, then random selection is adopted. 3.4 ....

S. Cheung and A. Kumar. Efficient quorumcast routing algorithms. In IEEE Proceedings of Infocom'94, pages 840--847, June 1994.

....minimum spanning tree. Up to constant factors in the approximation ratio, it is equivalent to ask for the shortest cycle (the k TSP problem) or shortest Steiner tree. Also inessential is the choice of metric. In fact, there has been a flurry of recent work on non geometric k MST problems [AABV94, CK94, RSM 94, ZL93] In this section, however, we shall focus on the Euclidean k MST formulation. The k MST problem was introduced by Fischetti et al. FHJM94] and Zelikovsky and Lozevanu [ZL93] and proved NP complete by those authors and also by Ravi et al. RSM 94] Ravi et al. devised an ....

S.Y. Cheung and A. Kumar. Efficient quorumcast routing algorithms. In Proc. IEEE INFOCOM '94 Conference on Computer Communications, volume 2, pages 840-- 847, 1994.

....reduces to O(k 1 4 ) 97] O(log k) 64, 87] O(log k log log n) 54] O(1) 21] 2 # 2 [89] and, very recently, 1 # (Arora, personal communication) We describe the 2 # 2 approximation algorithm, but the other results use similar methods. For related work on non geometric k MST problems see [13, 22, 30, 97, 116]. Mitchell [89] first restricts his attention to the rectilinear metric in the plane; the weight of a tree in this metric differs by its Euclidean weight by a factor of at most # 2, so this simplification entails only that factor loss in the overall approximation ratio of his algorithm. With this ....

S. Y. Cheung and A. Kumar. Efficient quorumcast routing algorithms. Proc. IEEE Conf. Computer Communications, 1994, vol. 2, pp. 840--847.

....nodes. A profit competitive strategy for this case is to find the largest subset of the multicast group that can be spanned by a steiner tree whose cost is below the profit scaled by the size of this subset [8] This is an NP hard problem. Heuristics for solving this problem were given in [18]; an O(log 2 n) approximation algorithm is described in [7] 6 Implementation Issues The previous sections presented the competitive routing and admission control strategies from a purely theoretical point of view. In this section we will discuss some of the issues involved in applying these ....

S.Y Cheung and A. Khumar. Efficient quorumcast routing algorithms. In Proc. INFOCOM '94, Volume 2, 1994.

....tree methods, can be used to multicast connections. Quorumcasting delivers a message from a single source node to any subset of jQj nodes in an n node network (jQj n) The problem of quorumcast routing is important in a number of distributed applications and the management of replicated data [4]. In distributed systems, for example, quorum consensus gives a general class of synchronization protocols. An operation proceeds to completion only after it coordinates with nodes that constitute a quorum set [2] The collection of quorum groups used by an operation is called a quorum set. A ....

....nodes. The number of routing trees that span the source node and the quorum set can be very large. The optimum routing tree is the one that has the minimum cost. As the multicast routing problem is NP complete, efficient optimal solutions to the quorumcast routing problem are unlikely to be found [4]. Cheung and Kumar [4] presented three heuristics: the Minimum Cost Path (MPH) heuristic, the Improved Minimum Path (IMP) heuristic, and the Modified Average Distance (MAD) heuristic, to find low cost solutions for the quorumcast routing problem. In the MPH heuristic, initially, only the source ....

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S.Y. Cheung and A. Kumar. Efficient quorumcast routing algorithms. In Proc. INFOCOM, pages 840--847, Toronto, Ontario, Canada, Jun. 1994.

....ff deadlock timeout is used, then the operation is restarted. Majority quorum consensus has been adopted to collect quorums from the top cluster for synchronous operations, although any other policy could have been used. Several quorum collection policies are discussed in the literature [AR91, CK94, GL92] Two straightforward solutions are to poll nodes serially one at a time until q nodes have responded (where q is the quorum size) or to send the request in parallel to all nodes. The first solution experiences excessive delay while the second incurs high traffic and causes congestion. ....

....then contacting more if report failures occur or to send to q ffl nodes in parallel. Since the extra nodes to send to are to account for failures, and since in our model it is assumed that failures do not occur, the adopted policy is to send the request to exactly q nodes in parallel. In [CK94] several heuristics have been presented to access q nodes out of m with minimum costs given the topology and communication cost between each pair of nodes. However, since nodes in the top cluster are assumed to be fully connected with the same link speeds, then random selection is adopted. ....

S. Cheung and A. Kumar. Efficient quorumcast routing algorithms. In IEEE Proceedings of Infocom'94, pages 840--847, June 1994.

....with improved approximation factors have since been discovered: Awerbuch et al. 2] obtain factor O(log 2 k) Rajagopalan and Vazirani [20] obtain O(logk) Blum, Ravi, and Vempala [7] obtain O(1) approximately factor 35) and, most recently, Garg [12] obtains a factor of 3. Cheung and Kumar [8] have also considered the problem, which they call the quorum cast problem and which arises in communication networks. Note that if k = n, the the k MST problem is simply the usual minimum spanning tree problem, which has efficient (polynomial time) exact solutions; thus, the complexity of the ....

S. Y. Cheung and A. Kumar, Efficient quorumcast routing algorithms, Proc. IEEE INFOCOM '94 Conference on Computer Communications, 2 (1994), pp. 840--847.

....problem is NP complete and has the same main difficulty faced by the above salesperson: which points to include and which to ignore In fact, the k MST problem nicely focuses on just that issue since once the set is determined, the least weight tree on that set is easy to find. Cheung and A. Kumar [8] call this problem the quorum cast problem, whose application are in the domain of communication networks. The bank robber problem is the following: given the map of a city including the amounts of money in each bank, and a car with bounded gas tank, the robber has to rob the maximum amount of ....

....of points in 2dimensional Euclidean space. Garg and Hochbaum [10] improved the ratio for the latter case to O(log k) which was then improved to a constant factor by Blum, Chalasani, and Vempala [6] Heuristics for problems described above have been given by Balas [4] and by Cheung and A. Kumar [8]. Results of this paper. In this paper, we describe an algorithm that achieves an approximation ratio O(log 2 k) for the k MST problem on general graphs, improving the previous bound of O( p k) 17] Our results hold for both the rooted and unrooted versions of the problem. In the rooted ....

S.Y. Cheung and A. Kumar. Efficient quorumcast routing algorithms. In Proceedings of INFOCOM '94, volume 2, pages 840--855, Toronto, 1994.

....Rajagopalan and Vazirani [20] obtain O(logk) In the time since our work first appeared (in [6] and [18] there have been further improvements in the approximation factors: Blum, Ravi, and Vempala [7] obtain a factor of 17, and, most recently, Garg [12] obtains a factor of 3. Cheung and Kumar [8] have also considered the problem, which they call the quorum cast problem and which arises in communication networks. Note that if k = n, the the k MST problem is simply the usual minimum spanning tree problem, which has efficient (polynomial time) exact solutions; thus, the complexity of the ....

S. Y. Cheung and A. Kumar, Efficient quorumcast routing algorithms, Proc. IEEE INFOCOM '94 Conference on Computer Communications, 2 (1994), pp. 840--847.

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S. Cheung, "Efficient Quorumcast Routing Algorithms," Proceedings of IEEE Infocom'94, Toronto, Canada, June 1994.

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