The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
Almost sure convergence of the minimum bipartite matching functional in Euclidean space
[article]
2002
arXiv
pre-print
Preserved Fulltext
., Y_N) be the minimum length of a bipartite matching between two sets of points in R^d, where X_1,..., X_N,... and Y_1,..., Y_N,... are random points independently and uniformly distributed in [0,1]^d ...
We prove that for d > 3, L_N/N^1-1/d converges with probability one to a constant β_MBM(d)>0 as N→∞ . ...
arXiv:math/0205140v1
fatcat:kjqhnjg77nbbdnjxbve7w7pkcq
Almost Sure Convergence of the Minimum Bipartite Matching Functional in Euclidean Space
2002
Combinatorica
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Asymptotically Optimal Algorithms for One-to-One Pickup and Delivery Problems With Applications to Transportation Systems
2013
IEEE Transactions on Automatic Control
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional ...
First, by embedding the problem within a stochastic framework, we present a novel algorithm for the SCP that: (i) is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the ...
For any finite partition of , almost surely. Proof: Let denote the optimal bipartite matching of . ...
doi:10.1109/tac.2013.2259993
fatcat:nwc7ajvk2jhg3anmcwakvvjp5y
Cost bounds for Pickup and Delivery Problems with application to large-scale transportation systems
2012
2012 American Control Conference (ACC)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The key strategy is to develop analytical bounds for the optimal cost of the Euclidean Stacker Crane Problem (ESCP), which represents a general static model for DRT systems. ...
In this paper, our aim is to bridge this gap for a rather general model of DRT systems, which takes the form of a generalized Dynamic Pickup and Delivery Problem. ...
ACKNOWLEDGMENTS The authors would like to thank Prof. Javed Aslam for suggesting the important connection between our lower bounds and the Wasserstain distance. ...
doi:10.1109/acc.2012.6315329
fatcat:rz4hyutym5fyhnrqv34isfi3ka
An asymptotically optimal algorithm for pickup and delivery problems
2011
IEEE Conference on Decision and Control and European Control Conference
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations. ...
Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world operations. ...
The Euclidean bipartite matching problem (EBMP), between sets X and Y of points in Euclidean space, is to find a permutation σ * (not necessarily unique) such that the sum of the Euclidean distances between ...
doi:10.1109/cdc.2011.6161406
dblp:conf/cdc/TreleavenPF11
fatcat:7qdjpiscm5h6hph4luyuwe4pdq
Page 2311 of Mathematical Reviews Vol. , Issue 2004c
[page]
2004
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
(F-PARIS11-TM; Orsay) Almost sure convergence of the minimum bipartite matching functional in Euclidean space. (English summary)
Combinatorica 22 (2002), no. 4, 523-530. ...
Summary: “Let Ly = Lygu(X%} Yy) be the min- imum length of a bipartite matching between two sets of points in R“, where X; a Yy,... are random points independently and uniformly distributed in [0, 1]/. ...
A Fast ℒpSpike Alignment Metric
2010
Neural Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. ...
We show how to implement a fast algorithm for the computation of this metric based on bipartite graph matching theory. * A. Dubbs is currently at the Mathematics Department, MIT. ...
Kaiser and the RU Outreach program for support and encouragement. This work was supported in part by the National Science Foundation under grant EF-0928723. ...
doi:10.1162/neco_a_00026
pmid:20804383
fatcat:amdsateo4zcvpcvbz7yqejzesi
On Minimum Spanning Trees for Random Euclidean Bipartite Graphs
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
We consider the minimum spanning tree problem on a weighted complete bipartite graph K_n_R, n_B whose n=n_R+n_B vertices are random, i.i.d. uniformly distributed points in the unit cube in d dimensions ...
and edge weights are the p-th power of their Euclidean distance, with p>0. ...
A full analysis was later performed by Steele [9] who proved that, if the Euclidean graph consists of n nodes, then for every 0 < p < d, almost sure convergence holds lim n→∞ C M ST (G n ) n 1−p/d = ...
arXiv:2107.08452v1
fatcat:7e222d6l6zgktkkv6blan5e5ze
Replica symmetry of the minimum matching
2012
Annals of Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
Abstract We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G. Parisi for the minimum matching problem in the pseudo-dimension d mean field model for d ≥ 1. ...
The case d = 1 corresponds to the π 2 /6-limit for the assignment problem proved by D. Aldous in 2001. ...
I thank the referees for suggestions that greatly improved the presentation. ...
doi:10.4007/annals.2012.175.3.2
fatcat:wlsy5tqx5zaq5b6qkzm5jpkome
Replica Symmetry and Combinatorial Optimization
[article]
2009
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
Parisi for minimum matching and the traveling salesman problem in the pseudo-dimension d mean field model for d\geq 1. ...
The case d=1 of minimum matching corresponds to the pi^2/6 limit for the assignment problem established by D. ...
Almost sure uniqueness of valuation is equivalent to the statement that the sequence converges pointwise, and this in turn implies that F is the unique fixed point of W θ . ...
arXiv:0908.1920v2
fatcat:tnaq7upd45ahzel5b3vh46fb54
A new framework for Euclidean summary statistics in the neural spike train space
2015
Annals of Applied Statistics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2015 pre-print arXiv:1506.03157v1 fatcat:kcnngbppinbcfksl3dgyyijovqOther Versions
Statistical analysis and inference on spike trains is one of the central topics in the neural coding. It is of great interest to understand the underlying structure of given neural data. ...
However, as those metrics lack certain Euclidean properties, the defined averages are nonunique, and do not share the conventional properties of a mean. ...
Almost
surely
Non-unique
Non-unique
Not known
Almost
surely
Table 1
we describe the schematic idea of incorporating the Isolated neuron
responses
(Not observed)
Background noise
(Observed ...
doi:10.1214/15-aoas847
fatcat:oj7kyuczwzh4hjidcl573hbr34
A Bayes consistent 1-NN classifier
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. ...
Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. ...
The algorithm invokes a minimum vertex cover routine, which by König's theorem is equivalent to maximum matching for bipartite graphs, and is computable in randomized time O(n 2.376 ) (Mucha and Sankowski ...
arXiv:1407.0208v4
fatcat:i7khxho6nbc73a7g5v4oruiydu
Fundamental performance limits and efficient polices for Transportation-On-Demand systems
2010
49th IEEE Conference on Decision and Control (CDC)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
as the inconvenience of privately-owned cars in metropolitan areas becomes excessive. ...
Specifically, we study TOD systems in the form of a unit-capacity, multiple-vehicle dynamic pick-up and delivery problem, whereby pick-up requests arrive according to a Poisson process and are randomly ...
Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the supporting organizations. ...
doi:10.1109/cdc.2010.5717552
dblp:conf/cdc/PavoneTF10
fatcat:trs52kaftngabpaql27teqd5zi
Limit theory of combinatorial optimization for random geometric graphs
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In the random geometric graph G(n,r_n), n vertices are placed randomly in Euclidean d-space and edges are added between any pair of vertices distant at most r_n from each other. ...
, bipartite matching and bipartite travelling salesman problems, for a general class of weight functions with at most polynomial growth of order d-ε, under thermodynamic scaling of the distance parameter ...
Here we obtain LLNs under thermodynamic scaling for a general class of weight functions f , not only for the TSP but also for the minimum-weight matching (MM), minimum spanning tree (MST) and minimum bipartite ...
arXiv:2006.14915v1
fatcat:uk7mnj3fxjctpat3u5kc6pn334
Methods for computing state similarity in Markov Decision Processes
[article]
2012
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We obtain in this manner a variety of distance functions for MDP state aggregation, which differ in the tradeoff between time and space complexity, as well as the quality of the aggregation. ...
A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. ...
Acknowledgments This work has been supported in part by funding from NSERC and CFI. ...
arXiv:1206.6836v1
fatcat:kpl4f6g7sfbrpkudsfianqqoue
« Previous
Showing results 1 — 15 out of 711 results