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Probabilistic Subgraph Matching Based on Convex Relaxation [chapter]

Christian Schellewald, Christoph Schnörr
2005 Lecture Notes in Computer Science  
We present a novel approach to the matching of subgraphs for object recognition in computer vision.  ...  For the resulting quadratic integer program, a mathematically tight relaxation is derived by exploiting the degrees of freedom of the embedding space of positive semidefinite matrices.  ...  The present paper is an attempt to overcome this limitation by a novel optimization approach to subgraph matching.  ... 
doi:10.1007/11585978_12 fatcat:un4ojokbnnb47limhmm5h727p4

A Convex Relaxation Bound for Subgraph Isomorphism

Christian Schellewald
2012 International Journal of Combinatorics  
The bound is based on a semidefinite programming relaxation of a combinatorial optimisation formulation for subgraph isomorphism and is explained in detail.  ...  Therefore, for problem instances with a lower bound that is larger than zero this represents a proof that a subgraph isomorphism can not exist.  ...  The bound can be computed with standard methods for semidefinite programs see, e.g., [18] [19] [20] .  ... 
doi:10.1155/2012/908356 fatcat:sf77jmkh4ffcxglc3f2audkmzq

Structure preserving embedding

Blake Shaw, Tony Jebara
2009 Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09  
SPE is formulated as a semidefinite program that learns a low-rank kernel matrix constrained by a set of linear inequalities which captures the connectivity structure of the input graph.  ...  SPE is implemented in MATLAB as a Semidefinite Program using CSDP and SDP-LR (Burer & Monteiro, 2003) and has complexity similar to other dimensionality reduction SDPs such as Semidefinite Embedding.  ...  We present an adaptation of MVU called MVU+SP, that simply adds the kNN structure preserving constraints to the MVU semidefinite program.  ... 
doi:10.1145/1553374.1553494 dblp:conf/icml/ShawJ09 fatcat:fuav2vglazadxoowayaaj34woi

Guaranteed clustering and biclustering via semidefinite programming

Brendan P. W. Ames
2013 Mathematical programming  
This approach also yields a semidefinite relaxation for the biclustering problem with similar recovery guarantees.  ...  In this paper, we establish conditions ensuring exact recovery of the densest k cliques of a given graph from the optimal solution of a particular semidefinite program.  ...  This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation, and by a Postgraduate Scholarship from NSERC (Natural Science  ... 
doi:10.1007/s10107-013-0729-x fatcat:6vwqvemewvb2vaxhd2ysdlammm

A randomized 1.885903-approximation algorithm for the minimum vertex cover problem [article]

Majid Zohrehbandian
2022 Zenodo  
In this paper, by a combination of a well-known semidefinite programming formulation and a rounding procedure, along with satisfying new properties, we introduce an approximation algorithm for the vertex  ...  cover problem with a performance ratio of on arbitrary graphs, en route answering an open question about the unique games conjecture.  ...  and objective value , and for solving the problem, we use the well known semidefinite programming (SDP) formulation as follows: Theorem 1.  ... 
doi:10.5281/zenodo.6512073 fatcat:sokwy77oynddzkkrxuytgqtfmq

Positive semidefinite propagation time

Nathan Warnberg
2016 Discrete Applied Mathematics  
First assume H is disconnected with vertices {1, 2, . . . , n} and let G = (H, K n , µ) be a matching graph. K n is a subgraph so by Theorem 2.3.4, n − 1 ≤ Z + (G).  ...  The program, in conjunction with the orthogonal representation method, establishes the positive semidefinite minimum rank for all graphs of order 7 or less.  ... 
doi:10.1016/j.dam.2015.04.008 fatcat:afciylcndja73diu2panv4r7kq

Turán densities of hypercubes [article]

Rahil Baber
2012 arXiv   pre-print
In this paper we describe a number of extensions to Razborov's semidefinite flag algebra method.  ...  We also show that the upper bound of the vertex Turán density of Q_3 can be improved to 0.76900, and that the vertex Turán density of Q_3 with one vertex removed is precisely 2/3.  ...  Note that finding the optimal upper bound of π(F ) is not a semidefinite programming problem but testing whether a specific value is an upper bound is a semidefinite programming problem.  ... 
arXiv:1201.3587v2 fatcat:iypfkyf7kvfsxmbalu623rssmu

Distributable Consistent Multi-Object Matching [article]

Nan Hu, Qixing Huang, Boris Thibert, Leonidas Guibas
2018 arXiv   pre-print
In this paper we propose an optimization-based framework to multiple object matching.  ...  Experiments on both synthetic and real-world datasets show that our framework is competitive against state-of-the-art multi-object matching techniques.  ...  On the other hand, solving semidefinite programs are computationally expensive.  ... 
arXiv:1611.07191v3 fatcat:jevqm6x6xbf6pcdon767uu6cvy

Exact Clustering of Weighted Graphs via Semidefinite Programming [article]

Aleksis Pirinen, Brendan Ames
2019 arXiv   pre-print
Specifically, the semidefinite relaxation is exact if the graph consists of k large disjoint subgraphs, corresponding to clusters, with weight concentrated within these subgraphs, plus a moderate number  ...  We establish that such subgraphs can be recovered from the solution of a particular semidefinite relaxation with high probability if the input graph is sampled from a distribution of clusterable graphs  ...  program by omitting the nonconvex rank constraint: max X∈Σ n + {Tr(W X) : Xe ≤ e, Tr X = k, X ≥ 0} . (5) We should note that the semidefinite program (5) is remarkably similar to the semidefinite relaxation  ... 
arXiv:1603.05296v5 fatcat:wi2vexdyj5bipmykzh4h3x5h4m

Product graph-based higher order contextual similarities for inexact subgraph matching

Anjan Dutta, Josep Lladós, Horst Bunke, Umapada Pal
2018 Pattern Recognition  
We use contextual similarities to construct an objective function and optimize it with a linear programming approach.  ...  Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG.  ...  Semidefinite programming Semidefinite programming is a general relaxation tool for approximating many combinatorial problems.  ... 
doi:10.1016/j.patcog.2017.12.003 fatcat:5ubxanxmtfazhgvb4ilarg2a6e

Distributable Consistent Multi-object Matching

Nan Hu, Qixing Huang, Boris Thibert, Leonidas Guibas
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
In this paper we propose an optimization-based framework to multiple object matching.  ...  Experiments on both synthetic and real-world datasets show that our framework is competitive against state-of-the-art multiobject matching techniques.  ...  On the other hand, solving semidefinite programs are computationally expensive.  ... 
doi:10.1109/cvpr.2018.00261 dblp:conf/cvpr/HuHTG18 fatcat:wjo6nlicazhmpmraoaozuidxme

New insight into introducing a (2-ℇ)-approximation ratio for minimum vertex cover problem [article]

Majid Zohrehbandian
2021 Zenodo  
Then, by a combination of semidefinite programming and a rounding procedure, along with satisfying the proposed assumptions, we introduce an approximation algorithm with a performance ratio of on arbitrary  ...  In this paper, we introduce a -approximation ratio on special graphs, and then, we show that on arbitrary graphs a -approximation ratio can be obtained by a combination of semidefinite programming (SDP  ...  In section 3, we propose a rounding procedure along with using the satisfying properties to propose an algorithm with a performance ratio smaller than on arbitrary graphs.  ... 
doi:10.5281/zenodo.5831865 fatcat:f5e2qmgcvfa5tix26kv32y2pyi

Page 7086 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Zeng Kun Xu (PRC-ZHNU; Jinhua) 95k:90065 90C27 Alizadeh, Farid (1-ICSI; Berkeley, CA) Interior point methods in semidefinite programming with applications to combinatorial optimization.  ...  condition that the matrix be positive semidefinite.  ... 

Page 5794 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
Given a directed graph G = (V, A) with node set V and arc set A, a subgraph S is called an equivalent subgraph, if S has a directed path between any pair of vertices for which there is a directed path  ...  (RC-NTHU-CS) Finding a complete matching with the maximum product on weighted bipartite graphs. (English summary) Comput. Math. Appl. 25 (1993), no. 5, 65-71.  ... 

On Computing Canonical Subsets of Graph-Based Behavioral Representations [chapter]

Walter C. Mankowski, Peter Bogunovich, Ali Shokoufandeh, Dario D. Salvucci
2009 Lecture Notes in Computer Science  
We are interested in automatically finding canonical behaviors: a small subset of behavioral protocols that is most representative of the full data set, providing a view of the data with as few protocols  ...  Form a semidefinite program with the combined objective of minimizing the weights of the intra edges and maximizing the weights of the cut edges (see Fig. 1 ). 3.  ...  Solve the semidefinite program from step 2 using the algorithm in [13] , obtaining positive semidefinite matrix X * . 4. Compute the Cholesky decomposition X * = V t V. 5.  ... 
doi:10.1007/978-3-642-02124-4_22 fatcat:dhy6k5gjyzgyrdldezf25kms7u
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