{"type":"ScholarlyArticle","title":"Diverse Approximations for Monotone Submodular Maximization Problems with a Matroid Constraint","authors":[{"name":"Anh Viet Do","slug":"anh-viet-do","given":"Anh Viet","family":"Do","affiliation":"School of Computer and Mathematical Sciences , The University of Adelaide"},{"name":"Mingyu Guo","slug":"mingyu-guo","given":"Mingyu","family":"Guo","affiliation":"School of Computer and Mathematical Sciences , The University of Adelaide"},{"name":"Aneta Neumann","slug":"aneta-neumann","given":"Aneta","family":"Neumann","affiliation":"School of Computer and Mathematical Sciences , The University of Adelaide"},{"name":"Frank Neumann","slug":"frank-neumann","given":"Frank","family":"Neumann","affiliation":"School of Computer and Mathematical Sciences , The University of Adelaide"}],"abstract":"Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its diverse solutions extension has not. In this study, we consider the most basic variants of submodular optimization, and propose two simple greedy algorithms, which are known to be effective at maximizing monotone submodular functions. These are equipped with parameters that control the trade-off between objective and diversity. Our theoretical contribution shows their approximation guarantees in both objective value and diversity, as functions of their respective parameters. Our experimental investigation with maximum vertex coverage instances demonstrates their empirical differences in terms of objective-diversity trade-offs.","doi":"10.24963/ijcai.2023/617","url":"https://ijcai.org/proceedings/2023/617","pdf":"https://ijcai.org/proceedings/2023/0617.pdf","markdown":"https://ijcai.org/proceedings/2023/617.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/617","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Search","track":"Main Track","number":617,"pages":{"first":5558,"last":5566},"keywords":["Search: S: Combinatorial search and optimisation","Search: S: Heuristic search"],"videos":[],"references":[{"position":1,"raw":"[Arrighi et al., 2021] Emmanuel Arrighi, Henning Fernau, Daniel Lokshtanov, Mateus de Oliveira Oliveira, and Petra Wolf. Diversity in kemeny rank aggregation: A param- eterized approach. In IJCAI, pages 10-16. International Joint Conferences on Artificial Intelligence Organization, August 2021.","title":"Diversity in kemeny rank aggregation: A parameterized approach","authors":"Emmanuel Arrighi, Henning Fernau, Daniel Lokshtanov, Mateus De Oliveira, Petra Oliveira, Wolf","year":"2021","venue":"International Joint Conferences on Artificial Intelligence Organization","doi":null,"url":null,"internal_url":"/proceedings/2021/2"},{"position":2,"raw":"[Baste et al., 2022] Julien Baste, Michael R. Fellows, Lars Jaffke, Tomáš Masařík, Mateus de Oliveira Oliveira, Gee- varghese Philip, and Frances A. Rosamond. Diversity of so- lutions: An exploration through the lens of fixed-parameter tractability theory. Artificial Intelligence, 303:103644, February 2022.","title":"Diversity of solutions: An exploration through the lens of fixed-parameter tractability theory","authors":"Julien Baste, R Michael, Lars Fellows, Tomáš Jaffke, Mateus Masařík, De Oliveira, Geevarghese Oliveira, Frances A Philip, Rosamond","year":"2022","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2020/156"},{"position":3,"raw":"[Calinescu et al., 2011] Gruia Calinescu, Chandra Chekuri, Martin Pál, and Jan Vondrák. Maximizing a monotone submodular function subject to a matroid constraint. SIAM Journal on Computing, 40(6):1740-1766, January 2011.","title":"Maximizing a monotone submodular function subject to a matroid constraint","authors":"Gruia Calinescu, Chandra Chekuri, Martin Pál, Jan Vondrák","year":"2011","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chandra and Halldórsson, 1996] Barun Chandra and Magnús M. Halldórsson. Facility dispersion and remote subgraphs. In SWAT, volume 1097 of Lecture Notes in Computer Science, pages 53-65. Springer Berlin Heidelberg, 1996.","title":"Facility dispersion and remote subgraphs","authors":"Barun Chandra, Magnús M Halldórsson","year":"1996","venue":"SWAT","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Chekuri and Kumar, 2004] Chandra Chekuri and Amit Ku- mar. Maximum coverage problem with group budget con- straints and applications. In APPROX-RANDOM, volume 3122 of Lecture Notes in Computer Science, pages 72-83. Springer Berlin Heidelberg, 2004.","title":"Chandra Chekuri and Amit Kumar. Maximum coverage problem with group budget constraints and applications","authors":"Kumar Chekuri","year":"2004","venue":"APPROX-RANDOM","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Chekuri and Pál, 2005] Chandra Chekuri and Martin Pál. A recursive greedy algorithm for walks in directed graphs. In FOCS, pages 245-253. IEEE, 2005.","title":"A recursive greedy algorithm for walks in directed graphs","authors":"Pál Chekuri, Chandra Chekuri, Martin Pál","year":"2005","venue":"FOCS","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Chekuri et al., 2014] Chandra Chekuri, Jan Vondrák, and Rico Zenklusen. Submodular function maximization via the multilinear relaxation and contention resolution schemes. SIAM Journal on Computing, 43(6):1831-1879, January 2014.","title":"Submodular function maximization via the multilinear relaxation and contention resolution schemes","authors":"Chandra Chekuri, Jan Vondrák, Rico Zenklusen","year":"2014","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Conforti and Cornuéjols, 1984] Michele Conforti and Gérard Cornuéjols. Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the rado-edmonds theorem. Discrete Applied Mathematics, 7(3):251-274, March 1984.","title":"Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the rado-edmonds theorem","authors":"Michele Conforti, Gérard Cornuéjols","year":"1984","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Cornuejols et al., 1977] Gerard Cornuejols, Marshall L. Fisher, and George L. Nemhauser. Location of bank ac- counts to optimize float: An analytic study of exact and approximate algorithms. Management Science, 23(8):789- 810, April 1977.","title":"Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms","authors":"Gerard Cornuejols, Marshall L Fisher, George L Nemhauser","year":"1977","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Danna et al., 2007] Emilie Danna, Mary Fenelon, Zonghao Gu, and Roland Wunderling. Generating multiple solutions for mixed integer programming problems. In IPCO, pages 280-294. Springer Berlin Heidelberg, 2007.","title":"Generating multiple solutions for mixed integer programming problems","authors":"Emilie Danna, Mary Fenelon, Zonghao Gu, Roland Wunderling","year":"2007","venue":"IPCO","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Eiter et al., 2009] Thomas Eiter, Esra Erdem, Halit Erdogan, and Michael Fink. Finding similar or diverse solutions in answer set programming. In Logic Programming, pages 342-356. Springer Berlin Heidelberg, 2009.","title":"Finding similar or diverse solutions in answer set programming","authors":"Thomas Eiter, Esra Erdem, Halit Erdogan, Michael Fink","year":"2009","venue":"Logic Programming","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Erkut, 1990] Erhan Erkut. The discrete p-dispersion prob- lem. European Journal of Operational Research, 46(1):48- 60, May 1990.","title":"The discrete p-dispersion problem","authors":"Erhan Erkut","year":"1990","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Feldman et al., 2020] Moran Feldman, Christopher Har- shaw, and Amin Karbasi. Simultaneous greedys: A swiss army knife for constrained submodular maximization. CoRR, abs/2009.13998, 2020.","title":"Simultaneous greedys: A swiss army knife for constrained submodular maximization","authors":"Moran Feldman, Christopher Harshaw, Amin Karbasi","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Fisher et al., 1978] M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey. An analysis of approximations for maximizing sub- modular set functions-II. In Mathematical Programming Studies, pages 73-87. Springer Berlin Heidelberg, 1978.","title":"An analysis of approximations for maximizing submodular set functions-II","authors":"M L Fisher, G L Nemhauser, L A Wolsey","year":"1978","venue":"Mathematical Programming Studies","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Fleischer et al., 2006] Lisa Fleischer, Michel X. Goemans, Vahab S. Mirrokni, and Maxim Sviridenko. Tight approxi- mation algorithms for maximum general assignment prob- lems. In SODA, pages 611-620. ACM Press, 2006.","title":"Tight approximation algorithms for maximum general assignment problems","authors":"Lisa Fleischer, Michel X Goemans, S Vahab, Maxim Mirrokni, Sviridenko","year":"2006","venue":"SODA","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Fomin et al., 2020] Fedor V. Fomin, Petr A. Golovach, Lars Jaffke, Geevarghese Philip, and Danil Sagunov. Diverse pairs of matchings. In ISAAC, pages 26:1-26:12, Dagstuhl, Germany, 2020. Schloss Dagstuhl -Leibniz-Zentrum für Informatik.","title":"Diverse pairs of matchings","authors":"V Fedor, Petr A Fomin, Lars Golovach, Geevarghese Jaffke, Danil Philip, Sagunov","year":"2020","venue":"ISAAC","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Fomin et al., 2021] Fedor V. Fomin, Petr A. Golovach, Fa- had Panolan, Geevarghese Philip, and Saket Saurabh. Di- verse collections in matroids and graphs. In STACS, pages 31:1-31:14, Dagstuhl, Germany, 2021. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.","title":"Diverse collections in matroids and graphs","authors":"V Fedor, Petr A Fomin, Fahad Golovach, Geevarghese Panolan, Saket Philip, Saurabh","year":"2021","venue":"STACS","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Gao et al., 2022] Jie Gao, Mayank Goswami, C. S. Karthik, Meng-Tsung Tsai, Shih-Yu Tsai, and Hao-Tsung Yang. Ob- taining approximately optimal and diverse solutions via dis- persion. In LATIN 2022: Theoretical Informatics, pages 222-239. Springer International Publishing, 2022.","title":"Obtaining approximately optimal and diverse solutions via dispersion","authors":"Jie Gao, Mayank Goswami, C S Karthik, Meng-Tsung Tsai, Shih-Yu Tsai, Hao-Tsung Yang","year":"2022","venue":"LATIN 2022: Theoretical Informatics","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Glover et al., 2000] Fred Glover, Arne LøKketangen, and David L. Woodruff. Scatter search to generate diverse MIP solutions. In Operations Research/Computer Science Interfaces Series, pages 299-317. Springer US, Boston, MA, 2000.","title":"Scatter search to generate diverse MIP solutions","authors":"Glover","year":"2000","venue":"Operations Research/Computer Science Interfaces Series","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Hanaka et al., 2021] Tesshu Hanaka, Yasuaki Kobayashi, Kazuhiro Kurita, and Yota Otachi. Finding diverse trees, paths, and more. Proceedings of the AAAI Conference on Artificial Intelligence, 35(5):3778-3786, May 2021.","title":"Finding diverse trees, paths, and more","authors":"Tesshu Hanaka, Yasuaki Kobayashi, Kazuhiro Kurita, Yota Otachi","year":"2021","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Hanaka et al., 2022a] Tesshu Hanaka, Masashi Kiyomi, Ya- suaki Kobayashi, Yusuke Kobayashi, Kazuhiro Kurita, and Yota Otachi. A framework to design approximation algo- rithms for finding diverse solutions in combinatorial prob- lems. CoRR, abs/2201.08940, 2022.","title":"A framework to design approximation algorithms for finding diverse solutions in combinatorial problems","authors":"Hanaka","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hanaka et al., 2022b] Tesshu Hanaka, Yasuaki Kobayashi, Kazuhiro Kurita, See Woo Lee, and Yota Otachi. Com- puting diverse shortest paths efficiently: A theoretical and experimental study. Proceedings of the AAAI Conference on Artificial Intelligence, 36(4):3758-3766, June 2022.","title":"Computing diverse shortest paths efficiently: A theoretical and experimental study","authors":"Hanaka","year":"2022","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Hao et al., 2020] Fei Hao, Zheng Pei, and Laurence T. Yang. Diversified top-k maximal clique detection in social internet of things. Future Generation Computer Systems, 107:408- 417, June 2020.","title":"Diversified top-k maximal clique detection in social internet of things","authors":"Fei Hao, Zheng Pei, Laurence T Yang","year":"2020","venue":"Future Generation Computer Systems","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Hebrard et al., 2005] Emmanuel Hebrard, Brahim Hnich, Barry O'Sullivan, and Toby Walsh. Finding diverse and sim- ilar solutions in constraint programming. In AAAI, pages 372-377. AAAI Press / The MIT Press, 2005.","title":"Finding diverse and similar solutions in constraint programming","authors":"Emmanuel Hebrard, Brahim Hnich, O' Barry, Toby Sullivan, Walsh","year":"2005","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Ingmar et al., 2020] Linnea Ingmar, Maria Garcia de la Banda, Peter J. Stuckey, and Guido Tack. Modelling diver- sity of solutions. Proceedings of the AAAI Conference on Artificial Intelligence, 34(02):1528-1535, April 2020.","title":"Modelling diversity of solutions","authors":"Linnea Ingmar, Maria Garcia De La Banda, Peter J Stuckey, Guido Tack","year":"2020","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Kashaev and Santiago, 2023] Danish Kashaev and Richard Santiago. A simple optimal contention resolution scheme for uniform matroids. Theoretical Computer Science, 940(Part A):81-96, 2023.","title":"Danish Kashaev and Richard Santiago. A simple optimal contention resolution scheme for uniform matroids","authors":"Santiago Kashaev","year":"2023","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Kempe et al., 2015] David Kempe, Jon Kleinberg, and Éva Tardos. Maximizing the spread of influence through a social network. Theory of Computing, 11(4):105-147, 2015.","title":"Maximizing the spread of influence through a social network","authors":"David Kempe, Jon Kleinberg, Éva Tardos","year":"2015","venue":"Theory of Computing","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Krause and Golovin, 2014] Andreas Krause and Daniel Golovin. Submodular function maximization. In Tractabil- ity, pages 71-104. Cambridge University Press, 2014.","title":"Submodular function maximization","authors":"Golovin Krause, Andreas Krause, Daniel Golovin","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Krause and Guestrin, 2005] Andreas Krause and Carlos Guestrin. UAI. In Proceedings of the Twenty-First Con- ference on Uncertainty in Artificial Intelligence, UAI'05, pages 324-331, Arlington, Virginia, USA, 2005. AUAI Press.","title":"UAI. In Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence, UAI'05","authors":"Guestrin Krause, Andreas Krause, Carlos Guestrin","year":"2005","venue":null,"doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Lee et al., 2010] Jon Lee, Vahab S. Mirrokni, Viswanath Nagarajan, and Maxim Sviridenko. Maximizing non- monotone submodular functions under matroid or knap- sack constraints. SIAM Journal on Discrete Mathematics, 23(4):2053-2078, January 2010.","title":"Maximizing nonmonotone submodular functions under matroid or knapsack constraints","authors":"Jon Lee, S Vahab, Mirrokni, Maxim Viswanath Nagarajan, Sviridenko","year":"2010","venue":"SIAM Journal on Discrete Mathematics","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Lin and Bilmes, 2010] Hui Lin and Jeff Bilmes. Multi- document summarization via budgeted maximization of submodular functions. In HLT-NAACL, pages 912-920, Los Angeles, California, June 2010. Association for Com- putational Linguistics.","title":"Multidocument summarization via budgeted maximization of submodular functions","authors":"Hui Lin, Jeff Bilmes","year":"2010","venue":"HLT-NAACL","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Lin and Bilmes, 2011] Hui Lin and Jeff Bilmes. A class of submodular functions for document summarization. In ACL, HLT '11, pages 510-520, USA, 2011. Association for Computational Linguistics.","title":"A class of submodular functions for document summarization","authors":"Hui Lin, Jeff Bilmes","year":"2011","venue":"ACL, HLT '11","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Mirzasoleiman et al., 2013] Baharan Mirzasoleiman, Amin Karbasi, Rik Sarkar, and Andreas Krause. Distributed sub- modular maximization: Identifying representative elements in massive data. In NIPS, NIPS'13, pages 2049-2057, Red","title":"Distributed submodular maximization: Identifying representative elements in massive data","authors":"Mirzasoleiman","year":"2013","venue":"NIPS, NIPS'13","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"Hook, NY, USA, 2013.","title":null,"authors":"N Y Hook, Usa","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Nadel, 2011] Alexander Nadel. Generating diverse solutions in SAT. In SAT, volume 6695 of Lecture Notes in Computer Science, pages 287-301. Springer Berlin Heidelberg, 2011.","title":"Generating diverse solutions in SAT","authors":"Alexander Nadel","year":"2011","venue":"SAT","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Nemhauser et al., 1978] G. L. Nemhauser, L. A. Wolsey, and M. L. Fisher. An analysis of approximations for max- imizing submodular set functions-I. Mathematical Pro- gramming, 14(1):265-294, December 1978.","title":"An analysis of approximations for maximizing submodular set functions-I","authors":"G L Nemhauser, L A Wolsey, M L Fisher","year":"1978","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Neumann et al., 2021] Aneta Neumann, Jakob Bossek, and Frank Neumann. Diversifying greedy sampling and evo- lutionary diversity optimisation for constrained monotone submodular functions. In GECCO. ACM, June 2021.","title":"Diversifying greedy sampling and evolutionary diversity optimisation for constrained monotone submodular functions","authors":"Aneta Neumann, Jakob Bossek, Frank Neumann","year":"2021","venue":"GECCO. ACM","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Oxley, 2011] James Oxley. Matroid Theory. Oxford Univer- sity Press, February 2011.","title":"James Oxley. Matroid Theory","authors":"Oxley","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Petit and Trapp, 2015] Thierry Petit and Andrew C. Trapp. Finding diverse solutions of high quality to constraint opti- mization problems. In IJCAI, IJCAI'15, pages 260--266. AAAI Press, 2015.","title":"Finding diverse solutions of high quality to constraint optimization problems","authors":"Thierry Petit, Andrew C Trapp","year":"2015","venue":"IJCAI, IJCAI'15","doi":null,"url":null,"internal_url":"/proceedings/2015/43"},{"position":40,"raw":"[Ravi et al., 1994] S. S. Ravi, Daniel J. Rosenkrantz, and Giri Kumar Tayi. Heuristic and special case algorithms for dispersion problems. Operations Research, 42(2):299- 310, April 1994.","title":"Heuristic and special case algorithms for dispersion problems","authors":"S S Ravi, Daniel J Rosenkrantz, Giri Kumar, Tayi","year":"1994","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Rossi and Ahmed, 2015] Ryan A. Rossi and Nesreen K. Ahmed. The network data repository with interactive graph analytics and visualization. In AAAI, 2015.","title":"The network data repository with interactive graph analytics and visualization","authors":"Ryan A Rossi, Nesreen K Ahmed","year":"2015","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"[Ruffini et al., 2019] Manon Ruffini, Jelena Vucinic, Simon de Givry, George Katsirelos, Sophie Barbe, and Thomas Schiex. Guaranteed diversity & quality for the weighted CSP. In ICTAI, pages 18-25. IEEE, November 2019.","title":"Guaranteed diversity & quality for the weighted CSP","authors":"Manon Ruffini, Jelena Vucinic, Simon De Givry, George Katsirelos, Sophie Barbe, Thomas Schiex","year":"2019","venue":"ICTAI","doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Schittekat and Sörensen, 2009] Patrick Schittekat and Ken- neth Sörensen. Supporting 3pl decisions in the automo- tive industry by generating diverse solutions to a large- scale location-routing problem. Operations Research, 57(5):1058-1067, 2009.","title":"Patrick Schittekat and Kenneth Sörensen. Supporting 3pl decisions in the automotive industry by generating diverse solutions to a largescale location-routing problem","authors":"Sörensen Schittekat","year":"2009","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":44,"raw":"[Tohidi et al., 2020] Ehsan Tohidi, Rouhollah Amiri, Mario Coutino, David Gesbert, Geert Leus, and Amin Karbasi. Submodularity in action: From machine learning to signal processing applications. IEEE Signal Processing Magazine, 37(5):120-133, September 2020.","title":"Submodularity in action: From machine learning to signal processing applications","authors":"Ehsan Tohidi, Rouhollah Amiri, Mario Coutino, David Gesbert, Geert Leus, Amin Karbasi","year":"2020","venue":"IEEE Signal Processing Magazine","doi":null,"url":null,"internal_url":null},{"position":45,"raw":"[Trapp and Konrad, 2015] Andrew C. Trapp and Renata A. Konrad. Finding diverse optima and near-optima to binary integer programs. IIE Transactions, 47(11):1300-1312, April 2015.","title":"Finding diverse optima and near-optima to binary integer programs","authors":"Andrew C Trapp, Renata A Konrad","year":"2015","venue":"IIE Transactions","doi":null,"url":null,"internal_url":null},{"position":46,"raw":"[Vondrák, 2013] Jan Vondrák. Symmetry and approximabil- ity of submodular maximization problems. SIAM Journal on Computing, 42(1):265-304, January 2013.","title":"Jan Vondrák. Symmetry and approximability of submodular maximization problems","authors":"Vondrák","year":"2013","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":47,"raw":"[Wang and Kuo, 1988] D.W. Wang and Yue-Sun Kuo. A study on two geometric location problems. Information Processing Letters, 28(6):281-286, August 1988.","title":"A study on two geometric location problems","authors":"D W Wang, Yue-Sun Kuo","year":"1988","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":48,"raw":"[Wang et al., 2013] Jia Wang, James Cheng, and Ada Wai- Chee Fu. Redundancy-aware maximal cliques. In Proceed- ings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD '13, pages 122-130. ACM, August 2013.","title":"Redundancy-aware maximal cliques","authors":"Jia Wang, James Cheng, Ada Wai, -Chee Fu","year":"2013","venue":"Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining, KDD '13","doi":null,"url":null,"internal_url":null},{"position":49,"raw":"[Xu and Li, 2006] Ke Xu and Wei Li. Many hard examples in exact phase transitions. Theoretical Computer Science, 355(3):291-302, April 2006.","title":"Many hard examples in exact phase transitions","authors":"Li ; ] Ke Xu, Wei Xu, Li","year":"2006","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":50,"raw":"[Yuan et al., 2015] Long Yuan, Lu Qin, Xuemin Lin, Lijun Chang, and Wenjie Zhang. Diversified top-k clique search. The VLDB Journal, 25(2):171-196, October 2015.","title":"Diversified top-k clique search","authors":"Long Yuan, Lu Qin, Xuemin Lin, Lijun Chang, Wenjie Zhang","year":"2015","venue":"The VLDB Journal","doi":null,"url":null,"internal_url":null},{"position":51,"raw":"[Zheng et al., 2017] Kaiping Zheng, Hongzhi Wang, Zhixin Qi, Jianzhong Li, and Hong Gao. A survey of query re- sult diversification. Knowledge and Information Systems, 51(1):1-36, September 2017.","title":"A survey of query result diversification","authors":"Kaiping Zheng, Hongzhi Wang, Zhixin Qi, Jianzhong Li, Hong Gao","year":"2017","venue":"Knowledge and Information Systems","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}