{"type":"ScholarlyArticle","title":"On Subset Selection with General Cost Constraints","authors":[{"name":"Chao Qian","slug":"chao-qian","given":"Chao","family":"Qian","affiliation":"UBRI , School of Computer Science and Technology , University of Science and Technology of China , Hefei 230027 , China"},{"name":"Jing-Cheng Shi","slug":"jing-cheng-shi","given":"Jing-Cheng","family":"Shi","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China"},{"name":"Yang Yu","slug":"yang-yu","given":"Yang","family":"Yu","affiliation":"National Key Laboratory for Novel Software Technology , Nanjing University , Nanjing 210023 , China"},{"name":"Ke Tang","slug":"ke-tang","given":"Ke","family":"Tang","affiliation":"UBRI , School of Computer Science and Technology , University of Science and Technology of China , Hefei 230027 , China"}],"abstract":"This paper considers the subset selection problem with a monotone objective function and a monotone cost constraint, which relaxes the submodular property of previous studies. We first show that the approximation ratio of the generalized greedy algorithm is $\\frac{\\alpha}{2}(1 \\textendash \\frac{1}{e^{\\alpha}})$ (where $\\alpha$ is the submodularity ratio); and then propose POMC, an anytime randomized iterative approach that can utilize more time to find better solutions than the generalized greedy algorithm. We show that POMC can obtain the same general approximation guarantee as the generalized greedy algorithm, but can achieve better solutions in cases and applications.","doi":"10.24963/ijcai.2017/364","url":"https://ijcai.org/proceedings/2017/364","pdf":"https://ijcai.org/proceedings/2017/0364.pdf","markdown":"https://ijcai.org/proceedings/2017/364.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/364","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":364,"pages":{"first":2613,"last":2619},"keywords":["Combinatorial & Heuristic Search: Combinatorial search/optimisation","Machine Learning: Machine Learning","Combinatorial & Heuristic Search: Heuristic Search"],"videos":[],"references":[{"position":1,"raw":"[Albert and Barabási, 2002] R. Albert and A.-L. Barabási. Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1):47, 2002.","title":"Statistical mechanics of complex networks","authors":"R Albert, A.-L Barabási","year":"2002","venue":"Reviews of Modern Physics","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Barbieri et al., 2012] N. Barbieri, F. Bonchi, and G. Manco. Topic-aware social influence propagation models. In Pro- ceedings of the 12th IEEE International Conference on Data Mining (ICDM'12), pages 81-90, Brussels, Bel- gium, 2012.","title":"Topic-aware social influence propagation models","authors":"N Barbieri, F Bonchi, G Manco","year":"2012","venue":"Proceedings of the 12th IEEE International Conference on Data Mining (ICDM'12)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Conforti and Cornuéjols, 1984] M. Conforti and G. 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, 1984.","title":"Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem","authors":"M Conforti, G Cornuéjols","year":"1984","venue":"Discrete Applied Mathematics","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Das and Kempe, 2011] A. Das and D. Kempe. Submodu- lar meets spectral: Greedy algorithms for subset selec- tion, sparse approximation and dictionary selection. In Proceedings of the 28th International Conference on Ma- chine Learning (ICML'11), pages 1057-1064, Bellevue, WA, 2011.","title":"Submodular meets spectral: Greedy algorithms for subset selection, sparse approximation and dictionary selection","authors":"A Das, D Kempe","year":"2011","venue":"Proceedings of the 28th International Conference on Machine Learning (ICML'11)","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Doerr et al., 2012] B. Doerr, D. Johannsen, and C. Winzen. Multiplicative drift analysis. Algorithmica, 64(4):673- 697, 2012.","title":"Multiplicative drift analysis","authors":"B Doerr, D Johannsen, C Winzen","year":"2012","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[ErdőS and Rényi, 1959] P. ErdőS and A. Rényi. On random graphs I. Publ. Math. Debrecen, 6:290-297, 1959.","title":"On random graphs I","authors":"P Erdős, A Rényi","year":"1959","venue":"Publ. Math. Debrecen","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Herer, 1999] Y. Herer. Submodularity and the traveling salesman problem. European Journal of Operational Re- search, 114(3):489-508, 1999.","title":"Submodularity and the traveling salesman problem","authors":"Y Herer","year":"1999","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hogg and Lerman, 2012] T. Hogg and K. Lerman. Social dynamics of digg. EPJ Data Science, 1(5):1-26, 2012.","title":"Social dynamics of digg","authors":"T Hogg, K Lerman","year":"2012","venue":"EPJ Data Science","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Iyer and Bilmes, 2013] R. Iyer and J. Bilmes. Submodu- lar optimization with submodular cover and submodular knapsack constraints. In Advances in Neural Information Processing Systems 26 (NIPS'13), pages 2436-2444, Lake Tahoe, NV, 2013.","title":"Submodular optimization with submodular cover and submodular knapsack constraints","authors":"R Iyer, J Bilmes","year":"2013","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Iyer et al., 2013] R. Iyer, S. Jegelka, and J. Bilmes. Curva- ture and optimal algorithms for learning and minimizing submodular functions. In Advances in Neural Information Processing Systems 26 (NIPS'13), pages 2742-2750, Lake Tahoe, NV, 2013.","title":"Curvature and optimal algorithms for learning and minimizing submodular functions","authors":"R Iyer, S Jegelka, J Bilmes","year":"2013","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Kempe et al., 2003] D. Kempe, J. Kleinberg, and É. Tardos. Maximizing the spread of influence through a social net- work. In Proceedings of the 9th ACM SIGKDD Interna- tional Conference on Knowledge Discovery and Data Min- ing (KDD'03), pages 137-146, Washington, DC, 2003.","title":"Maximizing the spread of influence through a social network","authors":"D Kempe, J Kleinberg, É Tardos","year":"2003","venue":"Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'03)","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Khuller et al., 1999] S. Khuller, A. Moss, and J. Naor. The budgeted maximum coverage problem. Information Pro- cessing Letters, 70(1):39-45, 1999.","title":"The budgeted maximum coverage problem","authors":"S Khuller, A Moss, J Naor","year":"1999","venue":"Information Processing Letters","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Krause and Guestrin, 2005] A. Krause and C. Guestrin. A note on the budgeted maximization of submodular func- tions. Technical Report No. CMU-CALD-05-103, 2005.","title":"A note on the budgeted maximization of submodular functions","authors":"A Krause, C Guestrin","year":"2005","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Krause et al., 2008] A. Krause, A. Singh, and C. Guestrin. Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies. Jour- nal of Machine Learning Research, 9:235-284, 2008.","title":"Near-optimal sensor placements in Gaussian processes: Theory, efficient algorithms and empirical studies","authors":"A Krause, A Singh, C Guestrin","year":"2008","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lin and Bilmes, 2010] H. Lin and J. Bilmes. Multi- document summarization via budgeted maximization of submodular functions. In Proceedings of the 11th Annual Conference of the North American Chapter of the Asso- ciation for Computational Linguistics (NAACL'10), pages 912-920, Los Angeles, CA, 2010.","title":"Multidocument summarization via budgeted maximization of submodular functions","authors":"H Lin, J Bilmes","year":"2010","venue":"Proceedings of the 11th Annual Conference of the North American Chapter of the Association for Computational Linguistics (NAACL'10)","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nemhauser and Wolsey, 1978] G. L. Nemhauser and L. A. Wolsey. Best algorithms for approximating the maximum of a submodular set function. Mathematics of Operations Research, 3(3):177-188, 1978.","title":"Best algorithms for approximating the maximum of a submodular set function","authors":"G L Nemhauser, L A Wolsey","year":"1978","venue":"Mathematics of Operations Research","doi":null,"url":null,"internal_url":null},{"position":17,"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, 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":18,"raw":"[Qian et al., 2015] C. Qian, Y. Yu, and Z.-H. Zhou. Subset selection by Pareto optimization. In Advances in Neu- ral Information Processing Systems 28 (NIPS'15), pages 1765-1773, Montreal, Canada, 2015.","title":"Subset selection by Pareto optimization","authors":"C Qian, Y Yu, Z.-H Zhou","year":"2015","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Qian et al., 2016] C. Qian, J.-C. Shi, Y. Yu, K. Tang, and Z.-H. Zhou. Parallel Pareto optimization for subset selec- tion. In Proceedings of the 25th International Joint Con- ference on Artificial Intelligence (IJCAI'16), pages 1939- 1945, New York, NY, 2016.","title":"Parallel Pareto optimization for subset selection","authors":"C Qian, J.-C Shi, Y Yu, K Tang, Z.-H Zhou","year":"2016","venue":"Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI'16)","doi":null,"url":null,"internal_url":"/proceedings/2016/277"},{"position":20,"raw":"[Rosenkrantz et al., 1977] D. J. Rosenkrantz, R. E. Stearns, and P. M. Lewis, II. An analysis of several heuristics for the traveling salesman problem. SIAM Journal on Com- puting, 6(3):563-581, 1977.","title":"An analysis of several heuristics for the traveling salesman problem","authors":"D J Rosenkrantz, R E Stearns, P M Lewis, I I","year":"1977","venue":"SIAM Journal on Computing","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Vondrák, 2010] J. Vondrák. Submodularity and curvature: The optimal algorithm. RIMS Kokyuroku Bessatsu B, 23:253-266, 2010.","title":"Submodularity and curvature: The optimal algorithm","authors":"J Vondrák","year":"2010","venue":"RIMS Kokyuroku Bessatsu B","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Zhang and Vorobeychik, 2016] H. Zhang and Y. Vorobey- chik. Submodular optimization with routing constraints. In Proceedings of the 30th AAAI Conference on Artificial In- telligence (AAAI'16), pages 819-826, Phoenix, AZ, 2016.","title":"Submodular optimization with routing constraints","authors":"H Zhang, Y Vorobeychik","year":"2016","venue":"Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI'16)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Zheng et al., 2013] Y. Zheng, F. Liu, and H.-P. Hsieh. U- air: When urban air quality inference meets big data. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'13), pages 1436-1444, Chicago, IL, 2013.","title":"Uair: When urban air quality inference meets big data","authors":"Y Zheng, F Liu, H.-P Hsieh","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}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}