Yair Bartal. Probabilistic approximations of metric spaces and its algorithmic applications. In IEEE FOCS, pages 184-193, 1996. Home/Search Document Details and Download
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A Data Tracking Scheme for General Networks - Rajmohan Rajaraman Andr'ea (2001) (13 citations) (Correct)
....scheme for arbitrary networks, that simultaneously achieves polylogarithmic approximations in stretch factors for access, insert and delete operations, as well as for local memory overhead per node. Our data tracking scheme is based on a randomized hierarchical decomposition technique of Bartal [8], that partitions the network into disjoint clusters at various degrees of locality. The protocol for accessing an object in our tracking scheme is to search for the object level by level, from the smallest clusters to the largest, until an object copy is found (if it exists) A challenge is then ....
....then one can drop another log n factor in all bounds for stretch and memory requirement (a simplified such scheme, which only provides guarantees on the expected cost of a read operation, is presented in Section 3) 1. 2 Related Work The clustering and decomposition techniques of Bartal [8, 9, 15] build on the seminal work of Awerbuch and Peleg [6] see also [4] who provide the first low diameter hierarchical decomposition for arbitrary networks. These clustering techniques have found several applications in distributed networks, and network algorithms such as maintaining routing tables ....
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In Proceedings of the Thirty-Seventh Annual IEEE Symposium on Foundations of Computer Science, pages 184--193, October 1996.
Network Topology Generators: Degree-Based vs. Structural - Hongsuda Tangmunarunkit.. (2002) (3 citations) (Correct)
....subgraph of n nodes within a ball around a node in the topology. Computing the distortion can be NP hard [36] For the results described in this paper, we use the smallest distortion obtained by applying our own heuristics. We also use a simple divide and conquer algorithm suggested by Bartal [5] . The tree has R(n) 1. The random graph and the mesh each have R(n) log n [19] Summary To more fully understand the distinctions made by our three metrics, we consider two other standard networks: a fully connected network and a linear chain. A fully connected network has extremely high ....
BARTAL, Y. Probabilistic Approximations of Metric Spaces and its Algorithmic Applications. In Proc. 37th IEEE Symposium on Foundations of Computer Science (October 1996), pp. 184--193.
On Directed Steiner Trees - Leonid Zosin Samir (2002) (3 citations) (Correct)
....subtractions on this path. Theorem 3.3. For the group Steiner tree problem, we can obtain a approximation algorithm with ratio O(log n log log n log k log ffi ) ffi is the diameter of the graph and k is the number of groups. Proof. We first convert an arbitrary metric to a tree metric (see [1, 3]) This causes an expected increase in length of each edge by an O(log n log log n) factor. Once the problem reduces to a tree, we can root the tree at r and direct all edges away from the root. For each group S j , we can create a new terminal j with edges from all nodes in S j to j. This graph ....
Y. Bartal, "Probabilistic approximations of metric spaces and its algorithmic applications", In Proceedings of the 37th Annual Symposium on Foundations of Computer Science, pages 184--193, (1996).
Simpler and Better Approximation Algorithms for Network.. - Gupta, Kumar, Roughgarden (2003) (155 citations) (Correct)
.... in detail here have presented successively superior algorithms for increasingly general versions of the problem [1, 2, 6, 10, 11, 12, 18, 20, 21, 26] For the SSBB problem considered here, the first nontrivial approximation was found by Awerbuch and Azar [2] using the tree embeddings of Bartal [5], and the first constant factor approximation was given by Guha et al. 12] The performance guarantee of the combinatorial algorithm of [12] was not stated explicitly, though Talwar [26] estimated it to be roughly 2000. Talwar [26] subsequently gave an LP rounding algorithm with an improved ....
Yair Bartal. Probabilistic approximations of metric spaces and its algorithmic applications. In Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, pages 184--193, 1996.
Flow Metrics - Bornstein, Vempala (Correct)
....between all pairs of vertices that are adjacent in the input graph. Similarly in the sparsest cut problem [9] the distance is also a cut metric. Other metrics that model interesting problems include Euclidean metrics (possibly of bounded dimension) 8, 2] path metrics [3, 6, 10] and tree metrics [1]. The problems modeled in this way are often NP hard (as in the case of the examples above) and one approach to solving them is to consider relaxations of the associated distances. In [9] cut metrics were relaxed to just metrics, i.e. distances satisfying the triangle inequality and this led to ....
Y. Bartal, \Probabilistic Approximation of Metric Spaces and its Algorithmic Applications, " Proc. of the 37th Ann. IEEE Symp. on Foundations of Computer Science, 184-193, 1996.
The Intrinsic Dimensionality of Graphs (Extended Abstract) - Krauthgamer, Lee (Correct)
.... 4, we employ the decomposition of [14] combined with the results of Section 3, to prove the conjecture for any family of graphs which excludes a fixed minor (this includes planar graphs, for instance) In Section 5, we modify a probabilistic decompositions of Linial and Saks [17] and of Bartal [3] for use with growthrestricted graphs. Our modifications are two fold. First, the parameters of our decomposition depend on # (and not on n = V as in [3] This is essential to our application. Secondly, our decomposition is local in the sense that events which are far apart (in G) are ....
....(this includes planar graphs, for instance) In Section 5, we modify a probabilistic decompositions of Linial and Saks [17] and of Bartal [3] for use with growthrestricted graphs. Our modifications are two fold. First, the parameters of our decomposition depend on # (and not on n = V as in [3]) This is essential to our application. Secondly, our decomposition is local in the sense that events which are far apart (in G) are mutually independent (a similar idea was used for a di#erent purpose in [17] As a result, we are able to apply the Lovasz Local Lemma, yielding decompositions ....
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In 37th Annual Symposium on Foundations of Computer Science, pages 184--193. IEEE, 1996.
Randomized k-Server Algorithms for Growth-Rate Bounded Graphs.. - Yair Cs Huji (2003) Self-citation (Bartal) (Correct)
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Yair Bartal. Probabilistic approximations of metric space and its algorithmic application. In 37th Annual Symposium on Foundations of Computer Science, pages 183--193, October 1996.
On Approximating Arbitrary Metrics by Tree Metrics - Bartal (1998) (87 citations) Self-citation (Bartal) (Correct)
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Y. Bartal. Probabilistic Approximation of Metric Spaces and its Algorithmic Applications. In Proc. of the 37th Ann. IEEE Symp. on Foundations of Computer Science, pages 184{ 193, October 1996.
Multi-Embedding and Path Approximation of Metric Spaces - Yair Bartal Manor (2003) (1 citation) Self-citation (Bartal) (Correct)
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Y. Bartal. Probabilistic approximations of metric space and its algorithmic application. In 37th FOCS, pages 183-193, 1996.
Limitations to Fréchet's Metric Embedding Method - Bartal, Linial, Mendel, Naor (2003) Self-citation (Bartal) (Correct)
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In 37th Annual Symposium on Foundations of Computer Science, pages 184-193, 1996.
Low Dimensional Embeddings of Ultrametrics - Bartal, Linial, Mendel, Naor (2004) (1 citation) Self-citation (Bartal) (Correct)
.... 2003 1 Introduction An ultrametric is a metric space (X, d) such that for every x, y, z X, d(x, z) max d(x, y) d(y, z) A more restricted class of finite metrics with an inherently hierarchical structure is that of k hierarchically well separated trees, defined as follows: Definition 1 [1] For k 1, a k hierarchically well separated tree (k HST) is a metric space whose elements are the leaves of a rooted finite tree T . To each vertex u T there is associated a label #(u) 0 such that #(u) 0 i# u is a leaf of T . It is required that if a vertex u is a child of a vertex v ....
Y. Bartal, Probabilistic approximation of metric spaces and its algorithmic applications, in: 37th Annual Symposium on Foundations of Computer Science, 1996, pp. 184--193.
On Metric Ramsey-type Dichotomies - Bartal, Linial, Mendel, Naor (2003) Self-citation (Bartal) (Correct)
....where c # (#) C # (#) depend only on # and satisfy max 0, 1 c log # c # (#) C # (#) min 1, 1 , with c, C 0 universal constants. In [4] a similar phase transition phenomenon is proved for embeddings in # p , p [1, 2) A natural refinement of ultrametrics was suggested in [1]. Definition 2 ( 1] For k 1, a k hierarchically well separated tree (k HST) is a metric space whose elements are the leaves of a rooted tree T . To each vertex u T , a label #(u) 0 is associated such that #(u) 0 i# u is a leaf of T . The labels are such that if a vertex u is a child of ....
....(#) depend only on # and satisfy max 0, 1 c log # c # (#) C # (#) min 1, 1 , with c, C 0 universal constants. In [4] a similar phase transition phenomenon is proved for embeddings in # p , p [1, 2) A natural refinement of ultrametrics was suggested in [1] Definition 2 ([1]) For k 1, a k hierarchically well separated tree (k HST) is a metric space whose elements are the leaves of a rooted tree T . To each vertex u T , a label #(u) 0 is associated such that #(u) 0 i# u is a leaf of T . The labels are such that if a vertex u is a child of a vertex v then ....
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In 37th Annual Symposium on Foundations of Computer Science (Burlington, VT, 1996.
On Metric Ramsey-Type Phenomena - Bartal, Linial, Mendel (3 citations) Self-citation (Bartal) (Correct)
....Ramsey type problems. In spite of the similarity of these problems, the results in the metric setting di er markedly from those for the linear setting. Finite metric spaces and their embeddings in other metric spaces have been intensively investigated in recent years. See for example the papers [3, 4, 13, 14, 23, 40, 50], the surveys [29, 35] and the book [41] for an exposition of most of the known results. We would like to particularly point out the fundamental article of M. Gromov [28] in which many of the modern concepts and problems in this area were systematically studied for the rst time (in fact, the ....
....is an ulrametric where vertices in the rooted tree are labelled by real numbers. The labels decrease by a factor k as you go down the levels away from the root. The distance between two leaves is the label of their lowest common ancestor. These decomposable metrics were introduced by Bartal [3]. Subsequently, he showed [4] that any n point metric can be O(log n log log n) probabilistically embeddable in ultrametrics. It is also shown in [4] that any ultrametric is k equivalent to a k HST. These results have found many unexpected algorithmic applications in recent years, mostly in ....
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In 37th Annual Symposium on Foundations of Computer Science (Burlington, VT, 1996.
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Yair Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In Proceedings of the 37th Annual Symposium on Foundations of Computer Science, 1996.
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Y. Bartal, "Probabilistic approximation of metric space and its algorithmic applications," in 37th Annual IEEE Symposium on Foundations of Computer Science, Oct. 1996.
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BARTAL, Y. Probabilistic Approximations of Metric Spaces and its Algorithmic Applications. In Proc. 37th IEEE Symposium on Foundations of Computer Science (October 1996), pp. 184--193.
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Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic application. In Proc. 37th IEEE Symp. on Foundation of Computer Science, pages 184--193, 1996.
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Y. Bartal. Probabilistic Approximations of Metric Spaces and its Algorithmic Applications. In Proc. 37th IEEE Symposium on Foundations of Computer Science, pages 184--193, October 1996.
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