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65
Universal Rigidity and Edge Sparsification for Sensor Network Localization
, 2009
"... Owing to their high accuracy and ease of formulation, there has been great interest in applying convex optimization techniques, particularly that of semidefinite programming (SDP) relaxation, to tackle the sensor network localization problem in recent years. However, a drawback of such techniques is ..."
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Cited by 8 (1 self)
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is that the resulting convex program is often expensive to solve. In order to speed up computation, various edge sparsification heuristics have been proposed, whose aim is to reduce the number of edges in the input graph. Although these heuristics do reduce the size of the convex program and hence making it faster
Conservative Edge Sparsification for Graph SLAM Node Removal
"... Abstract—This paper reports on optimizationbased methods for producing a sparse, conservative approximation of the dense potentials induced by node marginalization in simultaneous localization and mapping (SLAM) factor graphs. The proposed methods start with a sparse, but overconfident, ChowLiu tr ..."
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Cited by 3 (3 self)
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Abstract—This paper reports on optimizationbased methods for producing a sparse, conservative approximation of the dense potentials induced by node marginalization in simultaneous localization and mapping (SLAM) factor graphs. The proposed methods start with a sparse, but overconfident, ChowLiu tree approximation of the marginalization potential and then use optimizationbased methods to adjust the approximation so that it is conservative subject to minimizing the KullbackLeibler divergence (KLD) from the true marginalization potential. Results are presented over multiple realworld SLAM graphs and show that the proposed methods enforce a conservative approximation, while achieving low KLD from the true marginalization potential. I.
Generic FactorBased Node Marginalization and Edge Sparsification for PoseGraph SLAM
"... Abstract—This paper reports on a factorbased method for node marginalization in simultaneous localization and mapping (SLAM) posegraphs. Node marginalization in a posegraph induces fillin and leads to computational challenges in performing inference. The proposed method is able to produce a new ..."
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Cited by 11 (6 self)
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Abstract—This paper reports on a factorbased method for node marginalization in simultaneous localization and mapping (SLAM) posegraphs. Node marginalization in a posegraph induces fillin and leads to computational challenges in performing inference. The proposed method is able to produce a new set of constraints over the elimination clique that can represent either the true marginalization, or a sparse approximation of the true marginalization using a ChowLiu tree. The proposed algorithm improves upon existing methods in two key ways: First, it is not limited to strictly fullstate relativepose constraints and works equally well with other lowrank constraints such as those produced by monocular vision. Second, the new factors are produced in a way that accounts for measurement correlation, a problem ignored in other methods that rely upon measurement composition. We evaluate the proposed method over several realworld SLAM graphs and show that it outperforms other stateoftheart methods in terms of KullbackLeibler divergence. I.
Graph sparsification by effective resistances
 SIAM J. Comput
"... We present a nearlylinear time algorithm that produces highquality sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ǫ> 0, we produce a weighted subgraph H = (V, ˜ E, ˜w) of G such that  ˜ E  = O(n log n/ǫ 2) and for all vectors x ∈ R V (1 − ǫ) ∑ ..."
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Cited by 143 (9 self)
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) ∑ (x(u) − x(v)) 2 wuv ≤ ∑ (x(u) − x(v)) 2 ˜wuv ≤ (1 + ǫ) ∑ (x(u) − x(v)) 2 wuv. (1) uv∈E uv ∈ ˜ E This improves upon the sparsifiers constructed by Spielman and Teng, which had O(n log c n) edges for some large constant c, and upon those of Benczúr and Karger, which only satisfied (1) for x ∈ {0, 1
Improved Sparsification
, 1993
"... In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using ..."
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Cited by 29 (5 self)
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. Using our improved sparsification technique, we keep track of the following properties: minimum spanning forest, best swap, connectivity, 2edgeconnectivity, and bipartiteness, in time O(n 1/2 ) per edge insertion or deletion; 2vertexconnectivity and 3vertexconnectivity, in time O(n) per
Consistent sparsification for graph optimization
 in Proc. European Conf. Mobile Robotics
, 2013
"... Abstract — In a standard posegraph formulation of simultaneous localization and mapping (SLAM), due to the continuously increasing numbers of nodes (states) and edges (measurements), the graph may grow prohibitively too large for longterm navigation. This motivates us to systematically reduce the ..."
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Cited by 8 (1 self)
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Abstract — In a standard posegraph formulation of simultaneous localization and mapping (SLAM), due to the continuously increasing numbers of nodes (states) and edges (measurements), the graph may grow prohibitively too large for longterm navigation. This motivates us to systematically reduce
Spectral Sparsification and Restricted Invertibility
, 2010
"... In this thesis we prove the following two basic statements in linear algebra. Let B be an arbitrary n × m matrix where m ≥ n and suppose 0 < ε < 1 is given. 1. Spectral Sparsification. There is a nonnegative diagonal matrix Sm×m with at most ⌈n/ε2 ⌉ nonzero entries for which (1 − ε) 2BBT ≼ BSB ..."
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Cited by 11 (1 self)
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In this thesis we prove the following two basic statements in linear algebra. Let B be an arbitrary n × m matrix where m ≥ n and suppose 0 < ε < 1 is given. 1. Spectral Sparsification. There is a nonnegative diagonal matrix Sm×m with at most ⌈n/ε2 ⌉ nonzero entries for which (1 − ε) 2BBT
Sparsification a technique for speeding up dynamic graph algorithms.
 J. ACM,
, 1997
"... Abstract. We provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2edge connectivity, and bipartiteness in time O(n 1/ 2 ) per change; 3edge connect ..."
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Cited by 138 (18 self)
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Abstract. We provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2edge connectivity, and bipartiteness in time O(n 1/ 2 ) per change; 3edge
Sparsification of MotionPlanning Roadmaps by Edge Contraction
"... (RSEC), a simple and effective algorithm for reducing the size of a motionplanning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the new roadmap. The primitive operation used by RSEC is edge contraction—the contraction of a roadmap edge to a singl ..."
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Cited by 3 (2 self)
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(RSEC), a simple and effective algorithm for reducing the size of a motionplanning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the new roadmap. The primitive operation used by RSEC is edge contraction—the contraction of a roadmap edge to a
Results 1  10
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