Distance Oracles Beyond the Thorup–Zwick Bound - People - MIT
Distance Oracles Beyond the Thorup–Zwick Bound .... To achieve some guid- ance in .... all u ∈ B. Intuitively speaking, we grow balls around vertices of B ...
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How to Grow Your Balls - People
How to Grow Your Balls. (Distance Oracles Beyond the Thorup–Zwick Bound). Mihai Pătrașcu ... Beat [Thorup, Zwick] for graphs with ≪ n1+1/k edges? ~ ...
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Distance Oracles Beyond the Thorup–Zwick Bound - Stanford CS
Distance Oracles Beyond the Thorup–Zwick Bound .... some guidance in understanding distance oracles, we will prove a conditional lower bound. .... Our construction first considers the balls BA(u) for all u ∈ B. Intuitively speaking, we grow.
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Distance Oracles for Stretch Less Than 2 - Philip Brighten Godfrey
of stretch 3 , and a lower bound of Thorup and. Zwick  shows that oracles that return distances of stretch less than 3 must have size Ω(n2). However,.
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Improved Distance Oracles and Spanners for Vertex-Labeled Graphs
stretch of this construction grows exponentially in k, (2k −1). ... An approximate distance oracle for a given graph G = (V,E) is a processed data structure ... Thorup and Zwick showed how to construct for a given integer k ≥ 1, a (2k − 1)- ..... “sparse” areas, namely, balls around some node v such that |B(v, kd, G)| < d · ℓ1−1/k.
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Linear-Space Approximate Distance Oracles for Planar, Bounded
compact distance oracle of Thorup [Tho04] requires Ω(ϵ−1n lg n) space for n- ... Thorup and Zwick [TZ05] gave asymptotically almost optimal trade-offs for dis- ... weaker lower bound holds for sparse graphs: Sommer, Verbin, and Yu [SVY09] .... Each input-graph node v is associated with some decomposition-tree node,.
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Distance Oracles for Vertex-Labeled Graphs - University of Haifa
Theorem 1 (Thorup-Zwick Vertex-Label Distance Oracles). A vertex- ... While the stretch of this scheme grows exponentially in k, we are able to obtain the same .... Ai \ Ai+1, we define the ball of v to be the set of labels B(v) of all vertices in ..... M. Patrascu and L. Roditty, Distance oracles beyond the thorup-zwick bound, Proc.
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On Approximate Distance Labels and Routing Schemes with Affine
5/3) size, 2d + 1 affine stretch of the distance oracle of. Patraşcu and Roditty ... which is better than the stretch (2k − 1)d scheme of Thorup and Zwick. (J. ACM ' 05). .... The main technical contribution of  was a new ball growing protocol. Our ... The affine stretch of a routing scheme is a bound on the worst case route length ...
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A Sketch-Based Distance Oracle for Web-Scale Graphs - Microsoft
Feb 4, 2010 ... A Sketch-Based Distance Oracle for Web-Scale Graphs. Atish Das Sarma ... some kind of a request or a query that needs to be serviced .... the closest seed in each seed set, Thorup's and Zwick's al- ... beyond what we do in the online step. ..... returned distance estimate ˜d(u, v) is a lower bound on the.
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eCOMPASS eCOMPASS – TR – 025 Distance Oracles for Time
Jul 8, 2013 ... Time-dependent shortest paths, FIFO property, distance oracles. ... unreasonable in some application scenarios, e.g., for a traveler waiting at the dock of a .... deciding the specific times to grow balls at the destination because we simply do not know ...... Distance oracles beyond the Thorup–Zwick bound.
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Distance oracles are succinct data structures encoding shortest path information ... The FIFO property may seem unreasonable in some application scenarios, e.g. .... grow balls around vertices in the vicinity of the destination, because we simply ...... Patrascu, M., Roditty, L.: Distance oracles beyond the Thorup–Zwick bound.
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Fast Routing Table Construction Using Small Messages
erarchy in the spirit of Thorup-Zwick distance oracles . Our main challenge .... construction does not scale beyond the familiar lower bound of ˜Ω(. √ n), and a ...
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eCOMPASS eCOMPASS – TR – 050 ANALYSIS AND
Sep 24, 2014 ... some metric which assigns distance functions (rather than scalars) to the arcs, e.g., rep- resenting ... Distance oracles are succinct data structures encoding shortest path information among a carefully ..... settled by TDD, when growing a ball from (o, to). ..... Distance oracles beyond the Thorup–Zwick bound.
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beyond the Johnson-Lindenstrauss bound - Computer Sciences
Euclidean space where the metric is raised to some fractional power (the .... assuming the the metric obeys a certain weak growth rate condition, and ... This is reasonable, for instance, if we desire a compact distance oracle  for .... We start with some basic definitions: Let k ∈ N. For a point x ∈ X and r ≥ 0, the ball at ...
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On Compact Routing for the Internet
on all network topologies grow slower than linearly as func- .... more, routing on AS numbers requires some form of global directory to map IP .... knowledge of the network topology (or at least of distances between ... by 2δ balls of radius r. .... Thorup and Zwick ... 3 routing scheme because its RT size upper bound was nearly.
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Local Computation of Nearly Additive Spanners - LIFL
dG(u, v) denote the distance between u and v in G. An (α, β)-spanner of G is a spanning ... Thorup and Zwick  showed that (1 + ε, O(1/ε)k−2)- spanners with ...
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TRANSITIVE-CLOSURE SPANNERS∗ 1. Introduction. A spanner
a survey by Zwick ). ... paths [24, 25, 31], and algorithms for distance oracles [ 11, 65]. ... This upper bound is tight, in general, as witnessed by a complete bipartite graph with ... k-Spanner is in class IV, that is, inapproximable within nδ for some δ ∈ (0, 1), would ... Thorup  considered a special case of TC- spanners.
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On Compact Routing for the Internet - Caida
on all network topologies grow slower than linearly as func- tions of the .... more, routing on AS numbers requires some form of global directory to .... knowledge of the network topology (or at least of distances between ... by 2δ balls of radius r. ... This scaling performance can be extended beyond regular .... Thorup and Zwick.
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The multi-multiway cut problem - ScienceDirect.com
In this work we study the region growing rounding technique when applied to the ... and that under certain complexity assumptions it cannot be approximated beyond a ... This, in turn implies a natural separation oracle for the multi-multiway cut ... We define (an upper bound on) the weight of the edges 'leaving' these balls as ...
[ 1-s2.0-S0304397507000710-main.pdf?_tid=beba79f4-f75e-11e3-ad72-00000aacb35d&acdnat=1403147385_b2536a3a4d40971cc8c6dfb9ed5c4453 - Read/Download File