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An optimal minimum spanning tree algorithm
 J. ACM
, 2000
"... Abstract. We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decisiontree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning tree of a graph with n vertices and m edges that runs in time O(T ∗ (m, n)) where T ∗ is ..."
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Cited by 46 (10 self)
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Abstract. We establish that the algorithmic complexity of the minimum spanning tree problem is equal to its decisiontree complexity. Specifically, we present a deterministic algorithm to find a minimum spanning tree of a graph with n vertices and m edges that runs in time O(T ∗ (m, n)) where T ∗ is the minimum number of edgeweight comparisons needed to determine the solution. The algorithm is quite simple and can be implemented on a pointer machine. Although our time bound is optimal, the exact function describing it is not known at present. The current best bounds known for T ∗ are T ∗ (m, n) = �(m) and T ∗ (m, n) = O(m · α(m, n)), where α is a certain natural inverse of Ackermann’s function. Even under the assumption that T ∗ is superlinear, we show that if the input graph is selected from Gn,m, our algorithm runs in linear time with high probability, regardless of n, m, or the permutation of edge weights. The analysis uses a new martingale for Gn,m similar to the edgeexposure martingale for Gn,p.
On an Online Spanning Tree Problem in Randomly Weighted Graphs
 Combinatorics, Probability and Computing
, 2005
"... This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniform distributed over [0, 1]. An algorithm receives the edges one by one and has to decide immediately whether to includ ..."
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Cited by 3 (1 self)
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This paper is devoted to an online variant of the minimum spanning tree problem in randomly weighted graphs. We assume that the input graph is complete and the edge weights are uniform distributed over [0, 1]. An algorithm receives the edges one by one and has to decide immediately whether to include the current edge into the spanning tree or to reject it. The corresponding edge sequence is determined by some adversary. We propose an algorithm which achieves E [ALG] /E [OPT] = O (1) and E [ALG/OPT] = O (1) against a fair adaptive adversary, i.e., an adversary which determines the edge order online and is fair in a sense that he does not know more about the edge weights than the algorithm. Furthermore, we prove that no online algorithm performs better than E [ALG] /E [OPT] =# (log n) if the adversary knows the edge weights in advance. This lower bound is tight, since there is an algorithm which yields E [ALG] /E [OPT] = O (log n) against the strongest imaginable adversary. 1.
Centralitydriven Scalable Service Migration
"... Abstract—As social networking sites provide increasingly richer context, usercentric service development is expected to explode following the example of UserGenerated Content. A major challenge for this emerging paradigm is how to make these exploding in numbers, yet individually of vanishing dema ..."
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Cited by 2 (1 self)
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Abstract—As social networking sites provide increasingly richer context, usercentric service development is expected to explode following the example of UserGenerated Content. A major challenge for this emerging paradigm is how to make these exploding in numbers, yet individually of vanishing demand, services available in a costeffective manner; central to this task is the determination of the optimal service host location. We formulate this problem as a facility location problem and devise a distributed and highly scalable heuristic to solve it. Key to our approach is the introduction of a novel centrality metric. Wherever the service is generated, this metric helps to a) identify a small subgraph of candidate service host nodes with high service demand concentration capacity; b) project on them a reduced yet accurate view of the global demand distribution; and, ultimately, c) pave the service migration path towards the location that minimizes its aggregate access cost over the whole network. The proposed iterative service migration algorithm, called cDSMA, is extensively evaluated over both synthetic and realworld network topologies. In all cases, it achieves remarkable accuracy and robustness, clearly outperforming typical localsearch heuristics for service migration. Finally, we outline a realistic cDSMA protocol implementation with complexity up to two orders of magnitude lower than that of centralized solutions. I.
Scalable distributed service migration via 1 Complex Networks Analysis
, 1007
"... With social networking sites providing increasingly richer context, UserCentric Service (UCS) creation is expected to explode following a similar success path to UserGenerated Content. One of the major challenges in this emerging highly usercentric networking paradigm is how to make these explodi ..."
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Cited by 1 (1 self)
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With social networking sites providing increasingly richer context, UserCentric Service (UCS) creation is expected to explode following a similar success path to UserGenerated Content. One of the major challenges in this emerging highly usercentric networking paradigm is how to make these exploding in numbers yet, individually, of vanishing demand services available in a costeffective manner. Of prime importance to the latter (and focus of this paper) is the determination of the optimal location for hosting a UCS. Taking into account the particular characteristics of UCS, we formulate the problem as a facility location problem and devise a distributed and highly scalable heuristic solution to it. Key to the proposed approach is the introduction of a novel metric drawing on Complex Network Analysis. Given a current location of UCS, this metric helps to a) identify a small subgraph of nodes with high capacity to act as service demand concentrators; b) project on them a reduced yet accurate view of the global demand distribution that preserves the key attraction forces on UCS; and, ultimately, c) pave the service migration path towards its optimal location in the network. The proposed iterative UCS migration algorithm, called cDSMA, is extensively evaluated over synthetic and realworld network topologies. Our results show that cDSMA achieves high accuracy, fast convergence, remarkable insensitivity to the size and diameter of the network and resilience to inaccurate estimates of demands for UCS across the network. It is also shown to clearly outperform localsearch heuristics for service migration that constrain the subgraph to the immediate neighbourhood of the node currently hosting UCS. I.
Distributed Placement of Autonomic Internet Services
"... Abstract—The optimal placement of service facilities largely determines the capability of a data network to efficiently support its users ’ service demands. As centralized solutions over largescale distributed environments are extremely expensive, inefficient or even infeasible, distributed approac ..."
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Abstract—The optimal placement of service facilities largely determines the capability of a data network to efficiently support its users ’ service demands. As centralized solutions over largescale distributed environments are extremely expensive, inefficient or even infeasible, distributed approaches that rely on partial topology and demand information are the only credible approaches to the service placement problem, even at the expense of nonguaranteed optimality. In this paper, we propose a distributed service migration heuristic that iteratively solves instances of the 1median problem pushing progressively the service to more costeffective locations. Key to our algorithm is a trafficaware centrality metric, called weighted conditional betweenness centrality (wCBC), that captures the ability of a node to act as service demand concentrator and is employed in both selecting the nodes and setting their weights for the 1median problem instance. The assessment of our heuristic proceeds in two steps. First, assuming (ideal) knowledge of the invoked wCBC metric, we carry out a proofofconcept study that demonstrates the effectiveness of the heuristic over synthetic and realworld topologies as well as its advantages against comparable localsearchlike migration schemes. Next, we devise practical protocol implementations that approximate the heuristic using local measurements of transit traffic and preserve the excellent accuracy and fast convergence properties of the algorithm for different routing policies. Our solution applies to a broad range of networking scenarios, and is very relevant to the emerging trends for innetwork storage and involvement of the enduser in the creation and distribution of lightweight (autonomic) service facilities. 1