Weakly supervised segmentation with maximum bipartite graph matching by Liu, Weide, Zhang, Chi, Lin, Guosheng, Hung, Tzu-Yi, Miao, Chunyan

“…We model paired images containing common classes with a bipartite graph and use the maximum matching algorithm to locate corresponding areas in two images. …”
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Cycle systems in the complete bipartite graph plus a one-factor by Ling, San, Ma, Jun, Pu, Liqun, Shen, Hao

“…Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a one-factor added. …”
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Joint structured bipartite graph and row-sparse projection for large-scale feature selection by Dong, Xia, Nie, Feiping, Wu, Danyang, Wang, Rong, Li, Xuelong

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Multicomponent adversarial domain adaptation: a general framework by Yi, Chang'an, Chen, Haotian, Xu, Yonghui, Chen, Huanhuan, Liu, Yong, Tan, Haishu, Yan, Yuguang, Yu, Han

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Discovery of protein complexes with core-attachment structures from tandem affinity purification (TAP) data by Wu, Min, Li, Xiaoli, Kwoh, Chee Keong, Ng, See-Kiong, Wong, Limsoon

“…CACHET models the TAP data as a bipartite graph in which the two vertex sets are the baits and the preys, respectively. …”
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Ultra-scalable spectral clustering and ensemble clustering by Huang, Dong, Wang, Chang-Dong, Wu, Jiansheng, Lai, Jian-Huang, Kwoh, Chee-Keong

“…By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. …”
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Improved lower bounds for the 2-page crossing numbers of Km,n and Kn via semidefinite programming by Klerk, E. de., Pasechnik, Dmitrii V.

“…It has long been conjectured that the crossing numbers of the complete bipartite graph $K_{m,n}$ and of the complete graph $K_n$ equal $Z(m,n):=\bigl\lfloor\frac{n}{2}\bigr\rfloor \bigl\lfloor\frac{n-1}{2}\bigr\rfloor \bigl\lfloor\frac{m}{2}\bigr\rfloor \bigl\lfloor\frac{m-1}{2}\bigr\rfloor$ and $Z(n):=\frac{1}{4} \bigl\lfloor\frac{n}{2}\bigr\rfloor \bigl\lfloor\frac{n-1}{2}\bigr\rfloor \bigl\lfloor\frac{n-2}{2}\bigr\rfloor \bigl\lfloor\frac{n-3}{2}\bigr\rfloor$, respectively. …”
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Reduction of symmetric semidefinite programs using the regular representation by Klerk, Etienne de., Pasechnik, Dmitrii V., Schrijver, Alexander.

“…The technique is based on a low-order matrix ∗-representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices.We apply it to extending amethod of de Klerk et al. that gives a semidefinite programming lower bound to the crossing number of complete bipartite graphs. It implies that cr(K8,n) ≥ 2.9299n2−6n, cr(K9,n) ≥ 3.8676n2 − 8n, and (for any m ≥ 9) lim n→∞ cr(Km,n)/Z(m, n) ≥ 0.8594 m/m − 1, where Z(m,n) is the Zarankiewicz number [1/4(m-1)2][1/4(n-1)2], which is the conjectured value of cr(K m,n ). …”
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The price of connectivity in fair division by Bei, Xiaohui, Igarashi, Ayumi, Lu, Xinhang, Suksompong, Warut

“…In addition, we determine the optimal relaxation of envy-freeness that can be obtained with each graph for two agents, and characterize the set of trees and complete bipartite graphs that always admit an allocation satisfying envy-freeness up to one good (EF1) for three agents. …”
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