{"type":"ScholarlyArticle","title":"Exactly Solving Minimum Dominating Set and Its Generalization","authors":[{"name":"Ziliang Xiong","slug":"ziliang-xiong","given":"Ziliang","family":"Xiong","affiliation":"University of Electronic Science and Technology of China"},{"name":"Mingyu Xiao","slug":"mingyu-xiao","given":"Mingyu","family":"Xiao","affiliation":"University of Electronic Science and Technology of China"}],"abstract":"The Minimum Dominating Set Problem (MDSP) is an important NP-Hard optimization problem with many applications in various domains. This paper designs two exact algorithms for MDSP that use the same Branch-and-Bound framework. However, one uses LP relaxations as lower bounds for pruning the search space, and the other one is a pure combinatorial algorithm. The two algorithms possess a distinct advantage. Performance experiments on standard test datasets reveal that our combinatorial algorithm is over 1000 times faster than the previous state-of-the-art exact algorithm presented in IJCAI 2023, and our LP Relaxation algorithm can even enhance the speed of our combinatorial algorithm by over 100 times. However, our combinatorial algorithm still outperform the LP Relaxation algorithm on very dense graphs.","doi":"10.24963/ijcai.2024/780","url":"https://ijcai.org/proceedings/2024/780","pdf":"https://ijcai.org/proceedings/2024/0780.pdf","markdown":"https://ijcai.org/proceedings/2024/780.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/780","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Search","track":"Main Track","number":780,"pages":{"first":7056,"last":7064},"keywords":["Search: S: Combinatorial search and optimisation"],"videos":[],"references":[{"position":1,"raw":"Dataset: T1 |V | |E| BIBLP BIBCO BIBLP-IF BIBCO-IF EMOS 150 150 0.01 0.01 0.01 633.06(2) 25.03 150 250 0.03 1.41 0.03 28.02 334.58 150 500 8.18 2203.54(4) 10.46 1903.10(4) 2919.74(9) 150 750 11.17 2386.31(5) 12.37 1134.20(2) 3000.00(10) 150 1000 23.97 2224.23(4) 25.76 665.26(1) 3000.00(10) 150 2000 9.89 97.62 9.16 15.92 1851.73 150 3000 9.11 23.66 9.00 4.18 270.71 200 250 0.01 0.12 0.02 1840.26(5) 2900.47(7) 200 500 307.25(1) 2927.73(9) 18.07 3000.00(10) 3000.00(10) 200 750 166.89 3000.00(10) 200.27 3000.00(10) 3000.00(10) 200 1000 789.56 3000.00(10) 984.52 3000.00(10) 3000.00(10) 200 2000 1450.30 3000.00(10) 1559.50 3000.00(10) 3000.00(10) 200 3000 656.70 3000.00(10) 602.74 3000.00(10) 3000.00(10) 250 250 0.01 0.01 0.01 3000.00(10) 3000.00(10) 250 500 13.83 2783.49(9) 19.06 3000.00(10) 3000.00(10) 250 750 1030.34(1) 3000.00(10) 1054.77(1) 3000.00(10) 3000.00(10) 250 1000 2504.13(7) 3000.00(10) 2508.30(7) 3000.00(10) 3000.00(10) 300 300 0.01 0.01 0.01 3000.00(10) 3000.00(10) 300 500 5.80 2852.50(9) 5.36 3000.00(10) 3000.00(10) 300 750 1751.27(3) 3000.00(10) 2081.97(6) 3000.00(10) 3000.00(10) 800 1000 23.51 3000.00(10) 32.57 3000.00(10) 3000.00(","title":"Dataset: T1","authors":null,"year":null,"venue":"BIBLP BIBCO BIBLP-IF BIBCO-IF EMOS","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alber et al., 2004] Jochen Alber, Michael R. Fellows, and Rolf Niedermeier. Polynomial-time data reduction for dominating set. J. ACM, 51(3):363-384, 2004.","title":"Polynomial-time data reduction for dominating set","authors":"Alber","year":"2004","venue":"J. ACM","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Baïou and Barahona, 2014] Mourad Baïou and Francisco Barahona. The dominating set polytope via facility loca- tion. In Pierre Fouilhoux, Luis Eduardo Neves Gouveia, Ali Ridha Mahjoub, and Vangelis Th. Paschos, editors, Combinatorial Optimization -Third International Sympo- sium, ISCO 2014, Lisbon, Portugal, March 5-7, 2014, Re- vised Selected Papers, volume 8596 of Lecture Notes in Computer Science, pages 38-49. Springer, 2014.","title":"The dominating set polytope via facility location","authors":"Barahona Baïou, Mourad Baïou, Francisco Barahona","year":"2014","venue":"Combinatorial Optimization -Third International Symposium, ISCO 2014","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Cai et al., 2020] Shaowei Cai, Wenying Hou, Yiyuan Wang, Chuan Luo, and Qingwei Lin. Two-goal local search and inference rules for minimum dominating set. In Christian Bessiere, editor, Proceedings of the Twenty-Ninth Inter- national Joint Conference on Artificial Intelligence, IJCAI 2020, pages 1467-1473. ijcai.org, 2020.","title":"Two-goal local search and inference rules for minimum dominating set","authors":"Shaowei Cai, Wenying Hou, Yiyuan Wang, Chuan Luo, Qingwei Lin","year":"2020","venue":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020","doi":null,"url":null,"internal_url":"/proceedings/2020/204"},{"position":5,"raw":"[Chaurasia and Singh, 2015] Sachchida Nand Chaurasia and Alok Singh. A hybrid evolutionary algorithm with guided mutation for minimum weight dominating set. Appl. In- tell., 43(3):512-529, 2015.","title":"Sachchida Nand Chaurasia and Alok Singh. A hybrid evolutionary algorithm with guided mutation for minimum weight dominating set","authors":"Singh Chaurasia","year":"2015","venue":"Appl. Intell","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Courcelle, 1990] Bruno Courcelle. Graph rewriting: An al- gebraic and logic approach. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, pages 193-242. Elsevier and MIT Press, 1990.","title":"Graph rewriting: An algebraic and logic approach","authors":"Bruno Courcelle, Courcelle","year":"1990","venue":"Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cygan et al., 2011] Marek Cygan, Geevarghese Philip, Marcin Pilipczuk, Michal Pilipczuk, and Jakub Onufry Wojtaszczyk. Dominating set is fixed parameter tractable in claw-free graphs. Theor. Comput. Sci., 412(50):6982- 7000, 2011.","title":"Dominating set is fixed parameter tractable in claw-free graphs","authors":"Marek Cygan, Geevarghese Philip, Marcin Pilipczuk, Michal Pilipczuk, Jakub Onufry, Wojtaszczyk","year":"2011","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dinh et al., 2014] Thang N. Dinh, Yilin Shen, Dung T. Nguyen, and My T. Thai. On the approximability of posi- tive influence dominating set in social networks. J. Comb. Optim., 27(3):487-503, 2014.","title":"On the approximability of positive influence dominating set in social networks","authors":"N Thang, Yilin Dinh, Dung T Shen, My T Nguyen, Thai","year":"2014","venue":"J. Comb. Optim","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Ellis et al., 2004] John A. Ellis, Hongbing Fan, and Michael R. Fellows. The dominating set problem is fixed parameter tractable for graphs of bounded genus. J. Algo- rithms, 52(2):152-168, 2004.","title":"The dominating set problem is fixed parameter tractable for graphs of bounded genus","authors":"John A Ellis, Hongbing Fan, Michael R Fellows","year":"2004","venue":"J. Algorithms","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fan et al., 2019] Yi Fan, Yongxuan Lai, Chengqian Li, Nan Li, Zongjie Ma, Jun Zhou, Longin Jan Latecki, and Kaile Su. Efficient local search for minimum dominating sets in large graphs. In Guoliang Li, Jun Yang, João Gama, Jug- gapong Natwichai, and Yongxin Tong, editors, Database Systems for Advanced Applications -24th International Conference, DASFAA 2019, Chiang Mai, Thailand, April 22-25, 2019, Proceedings, Part II, volume 11447 of Lec- ture Notes in Computer Science, pages 211-228. Springer, 2019.","title":"Efficient local search for minimum dominating sets in large graphs","authors":"Yi Fan, Yongxuan Lai, Chengqian Li, Nan Li, Zongjie Ma, Jun Zhou, Longin, Jan Latecki, Kaile Su","year":"2019","venue":"Database Systems for Advanced Applications -24th International Conference, DASFAA 2019","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Garey and Johnson, 1979] Michael Randolph Garey and David Stifler Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., 1979.","title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","authors":"Johnson ; Garey, Randolph Michael, David Garey, Johnson Stifler","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Gast et al., 2015] Mikael Gast, Mathias Hauptmann, and Marek Karpinski. Inapproximability of dominating set on power law graphs. Theor. Comput. Sci., 562:436-452, 2015.","title":"Inapproximability of dominating set on power law graphs","authors":"Mikael Gast, Mathias Hauptmann, Marek Karpinski","year":"2015","venue":"Theor. Comput. Sci","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Hassani Karbasi and Ebrahimi Atani, 2013] Amir Has- sani Karbasi and Reza Ebrahimi Atani. Application of dominating sets in wireless sensor networks. International Journal of Security and its Applications, 7:185-202, 01 2013.","title":"Application of dominating sets in wireless sensor networks","authors":"Hassani Karbasi, Ebrahimi Atani, ; Amir, Hassani Karbasi, Reza Ebrahimi Atani","year":"2013","venue":"International Journal of Security and its Applications","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hedar and Ismail, 2010] Abdel-Rahman Hedar and Rashad Ismail. Hybrid genetic algorithm for minimum dominating set problem. In David Taniar, Osvaldo Gervasi, Beniamino Murgante, Eric Pardede, and Bernady O. Apduhan, edi- tors, Computational Science and Its Applications -ICCSA 2010, International Conference, Fukuoka, Japan, March 23-26, 2010, Proceedings, Part IV, volume 6019 of Lec- ture Notes in Computer Science, pages 457-467. Springer, 2010.","title":"Hybrid genetic algorithm for minimum dominating set problem","authors":"Ismail ; Abdel-Rahman Hedar, Rashad Hedar, Ismail","year":"2010","venue":"Computational Science and Its Applications -ICCSA 2010, International Conference","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Huangfu and Hall, 2018] Qi Huangfu and Julian Hall. Par- allelizing the dual revised simplex method. Math. Pro- gram. Comput., 10(1):119-142, 2018.","title":"Parallelizing the dual revised simplex method","authors":"Hall ; Huangfu, Qi Huangfu, Julian Hall","year":"2018","venue":"Math. Program. Comput","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Inza et al., 2024] Ernesto Parra Inza, Nodari Vakhania, José María Sigarreta Almira, and Frank Angel Hernández Mira. Exact and heuristic algorithms for the domination prob- lem. Eur. J. Oper. Res., 313(3):926-936, 2024.","title":"Exact and heuristic algorithms for the domination problem","authors":"Ernesto Parra Inza, Nodari Vakhania, José María Sigarreta, Almira, Frank Angel, Hernández Mira","year":"2024","venue":"Eur. J. Oper. Res","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Iwata, 2011] Yoichi Iwata. A faster algorithm for dominat- ing set analyzed by the potential method. In Dániel Marx and Peter Rossmanith, editors, Parameterized and Exact Computation -6th International Symposium, IPEC 2011, Saarbrücken, Germany, September 6-8, 2011. Revised Se- lected Papers, volume 7112 of Lecture Notes in Computer Science, pages 41-54. Springer, 2011.","title":"A faster algorithm for dominating set analyzed by the potential method","authors":"Yoichi Iwata","year":"2011","venue":"Parameterized and Exact Computation -6th International Symposium, IPEC 2011","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Jiang and Zheng, 2023] Hua Jiang and Zhifei Zheng. An exact algorithm for the minimum dominating set problem. In Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI 2023, 19th- 25th August 2023, Macao, SAR, China, pages 5604-5612.","title":"An exact algorithm for the minimum dominating set problem","authors":"Zheng ; ] Hua Jiang, Zhifei Jiang, Zheng","year":"2023","venue":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence, IJCAI 2023","doi":null,"url":null,"internal_url":"/proceedings/2023/622"},{"position":19,"raw":"[Jovanovic et al., 2010] Raka Jovanovic, Milan Tuba, and Dana Simian. Ant colony optimization applied to mini- mum weight dominating set problem. pages 322-326, 05 2010.","title":"Ant colony optimization applied to minimum weight dominating set problem","authors":"Jovanovic","year":"2010","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Karp, 1972] Richard M. Karp. Reducibility among combi- natorial problems. In Raymond E. Miller and James W. Thatcher, editors, Proceedings of a symposium on the Complexity of Computer Computations, held March 20- 22, 1972, at the IBM Thomas J. Watson Research Cen- ter, Yorktown Heights, New York, USA, The IBM Research Symposia Series, pages 85-103. Plenum Press, New York, 1972.","title":"Reducibility among combinatorial problems","authors":"Richard M Karp","year":"1972","venue":"Proceedings of a symposium on the Complexity of Computer Computations","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Lin et al., 2016] Geng Lin, Wenxing Zhu, and M. Montaz Ali. An effective hybrid memetic algorithm for the mini- mum weight dominating set problem. IEEE Trans. Evol. Comput., 20(6):892-907, 2016.","title":"An effective hybrid memetic algorithm for the mini-mum weight dominating set problem","authors":"Geng Lin, Wenxing Zhu, M Montaz Ali","year":"2016","venue":"IEEE Trans. Evol. Comput","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Potluri and Singh, 2011] Anupama Potluri and Alok Singh. Two hybrid meta-heuristic approaches for minimum dom- inating set problem. In Proceedings of the Second Interna- tional Conference on Swarm, Evolutionary, and Memetic Computing -Volume Part II, SEMCCO'11, page 97-104, Berlin, Heidelberg, 2011. Springer-Verlag.","title":"Anupama Potluri and Alok Singh. Two hybrid meta-heuristic approaches for minimum dominating set problem","authors":"Singh Potluri","year":"2011","venue":"Proceedings of the Second International Conference on Swarm, Evolutionary, and Memetic Computing -Volume Part II, SEMCCO'11","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Potluri and Singh, 2013] Anupama Potluri and Alok Singh. Hybrid metaheuristic algorithms for minimum weight dominating set. Appl. Soft Comput., 13(1):76-88, 2013.","title":"Hybrid metaheuristic algorithms for minimum weight dominating set","authors":"Anupama Potluri, Alok Singh","year":"2013","venue":"Appl. Soft Comput","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Raz and Safra, 1997] Ran Raz and Shmuel Safra. A sub- constant error-probability low-degree test, and a sub- constant error-probability PCP characterization of NP. In Frank Thomson Leighton and Peter W. Shor, editors, Pro- ceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, 1997, pages 475-484. ACM, 1997.","title":"Ran Raz and Shmuel Safra. A subconstant error-probability low-degree test, and a subconstant error-probability PCP characterization of NP","authors":"Safra Raz","year":"1997","venue":"Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing","doi":null,"url":null,"internal_url":null},{"position":25,"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":26,"raw":"[Sanchis, 2002] Laura A. Sanchis. Experimental analysis of heuristic algorithms for the dominating set problem. Algo- rithmica, 33(1):3-18, 2002.","title":"Experimental analysis of heuristic algorithms for the dominating set problem","authors":"Laura A Sanchis","year":"2002","venue":"Algorithmica","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Vazirani, 2001] Vijay V. Vazirani. Approximation algo- rithms. Springer, 2001.","title":"Approximation algorithms","authors":"Vijay V Vazirani","year":"2001","venue":null,"doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Wang et al., 2017] Yiyuan Wang, Shaowei Cai, and Ming- hao Yin. Local search for minimum weight dominating set with two-level configuration checking and frequency based scoring function. J. Artif. Intell. Res., 58:267-295, 2017.","title":"Local search for minimum weight dominating set with two-level configuration checking and frequency based scoring function","authors":"Wang","year":"2017","venue":"J. Artif. Intell. Res","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Wang et al., 2018] Yiyuan Wang, Shaowei Cai, Jiejiang Chen, and Minghao Yin. A fast local search algorithm for minimum weight dominating set problem on massive graphs. In Jérôme Lang, editor, Proceedings of the Twenty- Seventh International Joint Conference on Artificial Intel- ligence, IJCAI 2018, July 13-19, 2018, Stockholm, Swe- den, pages 1514-1522. ijcai.org, 2018.","title":"A fast local search algorithm for minimum weight dominating set problem on massive graphs","authors":"Wang","year":"2018","venue":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018","doi":null,"url":null,"internal_url":"/proceedings/2018/210"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}