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Sparsification of Decomposable Submodular Functions

Akbar Rafiey, Yuichi Yoshida
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions.  ...  To overcome this issue, we introduce the notion of sparsification for decomposable submodular functions whose objective is to obtain an accurate approximation of the original function that is a (weighted  ...  the best of our knowledge there is no prior work on sparsification algorithms for decomposable submodular functions.  ... 
doi:10.1609/aaai.v36i9.21275 fatcat:4tmtg2ekevd55lsofrk25qtf6m

Sparsification of Decomposable Submodular Functions [article]

Akbar Rafiey, Yuichi Yoshida
2022 arXiv   pre-print
The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions.  ...  To overcome this issue, we introduce the notion of sparsification for decomposable submodular functions whose objective is to obtain an accurate approximation of the original function that is a (weighted  ...  A novel class of submodular functions are decomposable submodular functions.  ... 
arXiv:2201.07289v1 fatcat:4gqsyaxoincvndnfhqgjz5dt3i

Augmented Sparsifiers for Generalized Hypergraph Cuts with Applications to Decomposable Submodular Function Minimization [article]

Austin R. Benson, Jon Kleinberg, Nate Veldt
2021 arXiv   pre-print
Finally, we apply our sparsification techniques to develop approximation algorithms for minimizing sums of cardinality-based submodular functions.  ...  This sparsification leads to faster approximate min s-t graph cut algorithms for certain classes of co-occurrence graphs.  ...  Decomposable Submodular Function Minimization Any submodular function can be minimized in polynomial time [34, 35, 63] , but the runtimes for general submodular functions are impractical in most cases  ... 
arXiv:2007.08075v2 fatcat:3zxg6oro6fgi3mpa5656lh7hgi

Hypergraph Cuts with Edge-Dependent Vertex Weights [article]

Yu Zhu, Santiago Segarra
2022 arXiv   pre-print
Moreover, we provide a way to construct submodular EDVWs-based splitting functions and prove that a hypergraph equipped with such splitting functions can be reduced to a graph sharing the same cut properties  ...  More precisely, we introduce a new class of hyperedge splitting functions that we call EDVWs-based, where the penalty of splitting a hyperedge depends only on the sum of EDVWs associated with the vertices  ...  In this case, the hypergraph minimum s-t cut problem can be solved using general submodular function minimizers [22, 27, 28, 29, 45, 49] or minimizers for decomposable submodular functions [18, 33,  ... 
arXiv:2201.06084v1 fatcat:khmicchdpvgmdno2zi26ycigeq

Scalable Combinatorial Bayesian Optimization with Tractable Statistical models [article]

Aryan Deshwal, Syrine Belakaria, Janardhan Rao Doppa
2020 arXiv   pre-print
We study the problem of optimizing expensive blackbox functions over combinatorial spaces (e.g., sets, sequences, trees, and graphs).  ...  First, reformulation of AFO problem as submodular relaxation with some unknown parameters, which can be solved efficiently using minimum graph cut algorithms.  ...  The views expressed are those of the authors and do not reflect the official policy or position of the NSF.  ... 
arXiv:2008.08177v1 fatcat:fadhmgy63vdupacdbmqjcskhfy

Sparsification of influence networks

Michael Mathioudakis, Francesco Bonchi, Carlos Castillo, Aristides Gionis, Antti Ukkonen
2011 Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '11  
Seeking a practical, scalable approach to sparsification, we devise Spine, a greedy, efficient algorithm with practically little compromise in quality.  ...  We claim that sparsification is a fundamental datareduction operation with many applications, ranging from visualization to exploratory and descriptive data analysis.  ...  This work was partially supported by the Spanish Centre for the Development of Industrial Technology under the CENIT program, project CEN-20101037, "Social Media" (www.cenitsocialmedia.es).  ... 
doi:10.1145/2020408.2020492 dblp:conf/kdd/MathioudakisBCGU11 fatcat:v35756h7xndrrgsosrkp63qgha

Maximizing the Weighted Number of Spanning Trees: Near-t-Optimal Graphs [article]

Kasra Khosoussi, Gaurav S. Sukhatme, Shoudong Huang, Gamini Dissanayake
2016 arXiv   pre-print
We reveal several new structures, such as the log-submodularity of the weighted number of spanning trees in connected graphs.  ...  Our results can be readily applied to a wide verity of applications involving graph synthesis and graph sparsification scenarios.  ...  We prove that the (weighted) number of spanning trees in connected graphs can be posed as a monotone log-submodular function.  ... 
arXiv:1604.01116v2 fatcat:winn2pzyvbhf5gvt43tj6w3ryy

Influence Propagation in Social Networks: A Data Mining Perspective

Francesco Bonchi
2011 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology  
With the success of online social networks and microblogs such as Facebook, Flickr and Twitter, the phenomenon of influence exerted by users of such platforms on other users, and how it propagates in the  ...  One of the key problems in this area is the identification of influential users, by targeting whom certain desirable marketing outcomes can be achieved.  ...  Kempe et al., however, showed that the function σ m (S) is monotone and submodular.  ... 
doi:10.1109/wi-iat.2011.286 dblp:conf/webi/Bonchi11 fatcat:wutoxda2hrg75iscjwp2hyc6my

Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components [article]

Nate Veldt, Austin R. Benson, Jon Kleinberg
2021 arXiv   pre-print
Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning.  ...  This variant is one of the most widely applied in practice, encompassing, e.g., common energy functions arising in image segmentation and recent generalized hypergraph cut functions.  ...  The past decade has witnessed several advances in faster algorithms for decomposable submodular function minimization (DSFM), i.e., minimizing a sum of simpler submodular functions [11, 26, 41, 31, 37  ... 
arXiv:2110.14859v1 fatcat:iyrk7mrpj5hmrcs7s7du63k6mu

Influence Propagation in Social Networks: A Data Mining Perspective

Francesco Bonchi
2011 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology  
With the success of online social networks and microblogs such as Facebook, Flickr and Twitter, the phenomenon of influence exerted by users of such platforms on other users, and how it propagates in the  ...  One of the key problems in this area is the identification of influential users, by targeting whom certain desirable marketing outcomes can be achieved.  ...  Kempe et al., however, showed that the function σ m (S) is monotone and submodular.  ... 
doi:10.1109/wi-iat.2011.292 fatcat:gdymrsxd3fgmhhhm5uaox2edbu

Maximizing the Number of Spanning Trees in a Connected Graph [article]

Huan Li, Stacy Patterson, Yuhao Yi, Zhongzhi Zhang
2018 arXiv   pre-print
We give both algorithmic and hardness results for this problem: - We give a greedy algorithm that, using submodularity, obtains an approximation ratio of (1 - 1/e - ϵ) in the exponent of the number of  ...  of an SDDM matrix.  ...  Lemma 3.1. log T (G + P ) is a monotone submodular function.  ... 
arXiv:1804.02785v2 fatcat:xi7w3e3s3ne7lfnk23tohibiuq

Tractable hypergraph properties for constraint satisfaction and conjunctive queries [article]

Dániel Marx
2011 arXiv   pre-print
Here we introduce a new hypergraph measure called submodular width, and show that bounded submodular width of H implies that CSP(H) is fixed-parameter tractable.  ...  In a matching hardness result, we show that if H has unbounded submodular width, then CSP(H) is not fixed-parameter tractable, unless the Exponential Time Hypothesis fails.  ...  . • Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain.  ... 
arXiv:0911.0801v3 fatcat:4hyeugfjovdjja7pfovpvzom34

Tractable hypergraph properties for constraint satisfaction and conjunctive queries

Dániel Marx
2010 Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10  
of partial solutions can be described by a submodular function.  ...  To prove these combinatorial results, we need to develop a theory of (multicommodity) flows on hypergraphs and vertex separators in the case when the function b(S) defining the cost of separator S is submodular  ...  -Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain.  ... 
doi:10.1145/1806689.1806790 dblp:conf/stoc/Marx10 fatcat:rue3f6bjjjgszgs37fq5bzitte

Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries

Dániel Marx
2013 Journal of the ACM  
of partial solutions can be described by a submodular function.  ...  To prove these combinatorial results, we need to develop a theory of (multicommodity) flows on hypergraphs and vertex separators in the case when the function b(S) defining the cost of separator S is submodular  ...  -Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain.  ... 
doi:10.1145/2535926 fatcat:z663q2gyc5a3fp4r26fnp4ivgi

Variational Graph Methods for Efficient Point Cloud Sparsification [article]

Daniel Tenbrinck, Fjedor Gaede, Martin Burger
2019 arXiv   pre-print
approximation based on the chosen regularization functional.  ...  The main contribution in this paper is a novel coarse-to-fine optimization scheme for point cloud sparsification, inspired by the efficiency of the recently proposed Cut Pursuit algorithm for total variation  ...  parameter, D is a differentiable, convex data fidelity term with the original data given as g, and R is a convex regularization functional, which is decomposable into differentiable and non-differentiable  ... 
arXiv:1903.02858v3 fatcat:52zqly764fgadckm4ph5h2ep7i
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