Insight Centre for Data Analytics

Transcription

1 Insight Centre for Data Analytics Recent Progress in Two-Sided Stable Matching Mohamed Siala May 2, 2018

2 Academic Career December 2011 to May 2015: PhD in Computer science, LAAS-CNRS, INSA Toulouse, France Funding: CNRS, Google, Midi-Pyrenees Since June 2015: Post Doctoral Researcher, Insight, Centre for Data Analytics, University College Cork, Ireland. Funding: Science Foundation Ireland 90% and UCC-UTRC 10%. Insight Centre for Data Analytics May 2, 2018 Slide 2

3 Research Areas & Applications Insight Centre for Data Analytics May 2, 2018 Slide 3

4 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Insight Centre for Data Analytics May 2, 2018 Slide 3

5 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Boolean SAT & Clause Learning: [CPAIOR 14, CP 15, CP 17, CPAIOR 17] Insight Centre for Data Analytics May 2, 2018 Slide 3

6 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Boolean SAT & Clause Learning: [CPAIOR 14, CP 15, CP 17, CPAIOR 17] Combinatorial optimisation, algorithmic complexity, operations research: [EAAI 15, Constraints 16, ICTAI 17, COCOA 17, IJCAI 17] Insight Centre for Data Analytics May 2, 2018 Slide 3

7 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Boolean SAT & Clause Learning: [CPAIOR 14, CP 15, CP 17, CPAIOR 17] Combinatorial optimisation, algorithmic complexity, operations research: [EAAI 15, Constraints 16, ICTAI 17, COCOA 17, IJCAI 17] Applications Insight Centre for Data Analytics May 2, 2018 Slide 3

8 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Boolean SAT & Clause Learning: [CPAIOR 14, CP 15, CP 17, CPAIOR 17] Combinatorial optimisation, algorithmic complexity, operations research: [EAAI 15, Constraints 16, ICTAI 17, COCOA 17, IJCAI 17] Applications Scheduling & Sequencing Problems: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, Constraints 16] Insight Centre for Data Analytics May 2, 2018 Slide 3

9 Research Areas & Applications Research Areas Constraint programming: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, CPAIOR 16, Constraints 16, CP 17, IJCAI 17, CPAIOR 17, CPAIOR 18] Boolean SAT & Clause Learning: [CPAIOR 14, CP 15, CP 17, CPAIOR 17] Combinatorial optimisation, algorithmic complexity, operations research: [EAAI 15, Constraints 16, ICTAI 17, COCOA 17, IJCAI 17] Applications Scheduling & Sequencing Problems: [CP 12, IJCAI 13, CPAIOR 14, Constraints 14, CP 15, EAAI 15, Constraints 16] Matching under Preferences: [CPAIOR 16, CP 17, IJCAI 17, ICTAI 17, COCOA 17] Insight Centre for Data Analytics May 2, 2018 Slide 3

10 Matching Under Preferences Insight Centre for Data Analytics May 2, 2018 Slide 4

11 Matching Under Preferences Insight Centre for Data Analytics May 2, 2018 Slide 4

12 Matching Under Preferences They are everywhere! (doctors to hospitals, house allocation, kidney exchange, etc) Insight Centre for Data Analytics May 2, 2018 Slide 4

13 Matching Under Preferences They are everywhere! (doctors to hospitals, house allocation, kidney exchange, etc) Robustness? Insight Centre for Data Analytics May 2, 2018 Slide 4

14 Matching Under Preferences They are everywhere! (doctors to hospitals, house allocation, kidney exchange, etc) Robustness? Modularity & Flexibility of CP to solve hard problems? Insight Centre for Data Analytics May 2, 2018 Slide 4

15 Matching Under Preferences Insight Centre for Data Analytics May 2, 2018 Slide 5

16 Matching Under Preferences Assign residents to hospitals Every resident has a personnel preference over hospitals Each hospital has a preference list over residents Insight Centre for Data Analytics May 2, 2018 Slide 5

17 Matching Under Preferences Assign students to universities Every student has a personnel preference over universities Each university has a preference list over students Insight Centre for Data Analytics May 2, 2018 Slide 5

18 Paper: Finding Robust Solutions to Stable Marriage Title: Finding Robust Solutions to Stable Marriage Authors: Begum Genc, Mohamed Siala, Barry O Sullivan, Gilles Simonin IJCAI- 17, August 2017, Melbourne, Australia Insight Centre for Data Analytics May 2, 2018 Slide 6

19 Context Insight Centre for Data Analytics May 2, 2018 Slide 7

20 Background Insight Centre for Data Analytics May 2, 2018 Slide 8

21 Background A set of men U = {m 1, m 2,..., m n1 } and a set of woman W = {w 1, w 2,..., w n2 } Insight Centre for Data Analytics May 2, 2018 Slide 8

22 Background A set of men U = {m 1, m 2,..., m n1 } and a set of woman W = {w 1, w 2,..., w n2 } Each person has an ordinal preference list over people of the opposite sex Insight Centre for Data Analytics May 2, 2018 Slide 8

23 Background A set of men U = {m 1, m 2,..., m n1 } and a set of woman W = {w 1, w 2,..., w n2 } Each person has an ordinal preference list over people of the opposite sex A matching M is a one-to-one correspondence between U and W Insight Centre for Data Analytics May 2, 2018 Slide 8

24 Background A set of men U = {m 1, m 2,..., m n1 } and a set of woman W = {w 1, w 2,..., w n2 } Each person has an ordinal preference list over people of the opposite sex A matching M is a one-to-one correspondence between U and W Insight Centre for Data Analytics May 2, 2018 Slide 8

25 Background A set of men U = {m 1, m 2,..., m n1 } and a set of woman W = {w 1, w 2,..., w n2 } Each person has an ordinal preference list over people of the opposite sex A matching M is a one-to-one correspondence between U and W A matching M is called stable if for every (m, w) M, if m prefers w to w, then (m, w ) M such that w prefers m to m if w prefers m to m, then (m, w ) M such that m prefers w to w Insight Centre for Data Analytics May 2, 2018 Slide 8

26 Motivation Insight Centre for Data Analytics May 2, 2018 Slide 9

27 Motivation Insight Centre for Data Analytics May 2, 2018 Slide 9

28 Overview of the contributions (a,b)-supermatch ([Ginsberg98supermodelsand, 07-hebrard-phd]) An (a, b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs Insight Centre for Data Analytics May 2, 2018 Slide 10

29 Overview of the contributions (a,b)-supermatch ([Ginsberg98supermodelsand, 07-hebrard-phd]) An (a, b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs Contributions (regarding the (1,b) case) Verification in polynomial time Three models to find the most robust solution Experimental study on random instances Insight Centre for Data Analytics May 2, 2018 Slide 10

30 Example m w m w m w m w m w m w m w This instance has 10 stable matchings Insight Centre for Data Analytics May 2, 2018 Slide 11

31 Dominance Relation of Stable Matchings Insight Centre for Data Analytics May 2, 2018 Slide 12

32 Dominance Relation of Stable Matchings Insight Centre for Data Analytics May 2, 2018 Slide 12

33 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 Insight Centre for Data Analytics May 2, 2018 Slide 13

34 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 Insight Centre for Data Analytics May 2, 2018 Slide 13

35 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 5, 0 6, 5 1, 4 Insight Centre for Data Analytics May 2, 2018 Slide 13

36 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 5, 4 6, 0 1, 5 Insight Centre for Data Analytics May 2, 2018 Slide 13

37 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 5, 4 6, 0 1, 5 The sequence ρ 1 = [ 1, 4, 5, 0, 6, 5 ] is called a rotation Insight Centre for Data Analytics May 2, 2018 Slide 13

38 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 5, 4 6, 0 1, 5 The sequence ρ 1 = [ 1, 4, 5, 0, 6, 5 ] is called a rotation 1, 4 is eliminated by ρ 1 Insight Centre for Data Analytics May 2, 2018 Slide 13

39 Rotation M 1 : 0, 2, 1, 4, 2, 6, 3, 3, 4, 1, 5, 0, 6, 5 M 2 : 0, 2, 1, 5, 2, 6, 3, 3, 4, 1, 5, 4, 6, 0 5, 4 6, 0 1, 5 The sequence ρ 1 = [ 1, 4, 5, 0, 6, 5 ] is called a rotation 1, 4 is eliminated by ρ 1 1, 5 is produced by ρ 1 Insight Centre for Data Analytics May 2, 2018 Slide 13

40 The Partial Order on Rotations Insight Centre for Data Analytics May 2, 2018 Slide 14

41 Rotation Graph Insight Centre for Data Analytics May 2, 2018 Slide 15

42 Closed Subset Insight Centre for Data Analytics May 2, 2018 Slide 16

43 Closed Subset Theorem [89-sm-book, 07-mm-matching] There is a one-to-one mapping between closed subsets and stable matchings Insight Centre for Data Analytics May 2, 2018 Slide 16

44 Verification Insight Centre for Data Analytics May 2, 2018 Slide 17

45 Verification M: a stable matching b: is an integer Insight Centre for Data Analytics May 2, 2018 Slide 17

46 Verification M: a stable matching b: is an integer S: closed subset of M m, w : couple to break-up ρ p: rotation that produces m, w ρ e: rotation that eliminates m, w Insight Centre for Data Analytics May 2, 2018 Slide 17

47 Verification M: a stable matching b: is an integer S: closed subset of M m, w : couple to break-up ρ p: rotation that produces m, w ρ e: rotation that eliminates m, w S UP : The largest closed subset S that does not include ρ p S DOWN : The smallest closed subset S that includes ρ e Insight Centre for Data Analytics May 2, 2018 Slide 17

48 Verification M: a stable matching b: is an integer S: closed subset of M m, w : couple to break-up ρ p: rotation that produces m, w ρ e: rotation that eliminates m, w S UP : The largest closed subset S that does not include ρ p S DOWN : The smallest closed subset S that includes ρ e Insight Centre for Data Analytics May 2, 2018 Slide 17

49 Robust Solutions Problem Given a SM instance, find the most robust stable matching. That is, find a (1,b)-supermatch such that b is minimum Insight Centre for Data Analytics May 2, 2018 Slide 18

50 Robust Solutions Problem Given a SM instance, find the most robust stable matching. That is, find a (1,b)-supermatch such that b is minimum NP-Hard! On the Complexity of Robust Stable Marriage, Begum Genc, Mohamed Siala, Gilles Simonin, Barry O Sullivan, COCOA 17, December 2017, Shanghai, China. Insight Centre for Data Analytics May 2, 2018 Slide 18

51 Local Search: Key Idea Random solutions based on random closed subsets The evaluation of a solution is based on the verification procedure The neighbourhood of a solution S is defined by adding/removing one rotation to S Insight Centre for Data Analytics May 2, 2018 Slide 19

52 Genetic Algorithm Random population based on random closed subsets The evaluation of a solution is based on the verification procedure Crossover: Given S 1 and S 2, pick at random ρ 1 S 1, then add ρ 1 and all its predecessors to S 2 Mutation: Given S and a random rotation ρ, if ρ / S, then add ρ and all its predecessors to S. Otherwise, remove ρ and all its successors to S Insight Centre for Data Analytics May 2, 2018 Slide 20

53 Experimental Study Insight Centre for Data Analytics May 2, 2018 Slide 21

54 Experimental Study 1,000 CP GA LS CPU Time Objective ratio Insight Centre for Data Analytics May 2, 2018 Slide 21

55 Experimental Study: Large Instances 1,000 GA LS CPU Time Objective ratio Insight Centre for Data Analytics May 2, 2018 Slide 22

56 Paper: Rotation-Based Formulation for Stable Matching Title: Rotation-Based Formulation for Stable Matching Authors: Mohamed Siala and Barry O Sullivan, CP 17, August 2017, Melbourne, Australia Insight Centre for Data Analytics May 2, 2018 Slide 23

57 Context Insight Centre for Data Analytics May 2, 2018 Slide 24

58 Context Many to many stable matching Insight Centre for Data Analytics May 2, 2018 Slide 24

59 Context Many to many stable matching as a global constraint Insight Centre for Data Analytics May 2, 2018 Slide 24

60 Context Many to many stable matching as a global constraint Modularity and Efficiency to tackle hard variants Insight Centre for Data Analytics May 2, 2018 Slide 24

61 Context Many to many stable matching as a global constraint Modularity and Efficiency to tackle hard variants Insight Centre for Data Analytics May 2, 2018 Slide 24

62 Key Idea: Rotation-based Reformulation Theorem [89-sm-book, 07-mm-matching] There is a one-to-one mapping between closed subsets and stable matchings Insight Centre for Data Analytics May 2, 2018 Slide 25

63 Key Idea: Rotation-based Reformulation Theorem [89-sm-book, 07-mm-matching] There is a one-to-one mapping between closed subsets and stable matchings Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Insight Centre for Data Analytics May 2, 2018 Slide 25

64 Key Idea: Rotation-based Reformulation Theorem [89-sm-book, 07-mm-matching] There is a one-to-one mapping between closed subsets and stable matchings Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 Insight Centre for Data Analytics May 2, 2018 Slide 25

65 Key Idea: Rotation-based Reformulation Theorem [89-sm-book, 07-mm-matching] There is a one-to-one mapping between closed subsets and stable matchings Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 Express the relationship between the two sets of variables Insight Centre for Data Analytics May 2, 2018 Slide 25

66 Important Notions & Properties Insight Centre for Data Analytics May 2, 2018 Slide 26

67 Important Notions & Properties A pair is stable when it belongs to a stable matching Insight Centre for Data Analytics May 2, 2018 Slide 26

68 Important Notions & Properties A pair is stable when it belongs to a stable matching Some pairs are non-stable Insight Centre for Data Analytics May 2, 2018 Slide 26

69 Important Notions & Properties A pair is stable when it belongs to a stable matching Some pairs are non-stable Some pairs are fixed Insight Centre for Data Analytics May 2, 2018 Slide 26

70 Important Notions & Properties A pair is stable when it belongs to a stable matching Some pairs are non-stable Some pairs are fixed Insight Centre for Data Analytics May 2, 2018 Slide 26

71 Important Notions & Properties A pair is stable when it belongs to a stable matching Some pairs are non-stable Some pairs are fixed In O(L) time, one can compute: M 0, M z The fixed, stable and non-stable pairs The set of rotations The graph poset ρ ew,f and ρ pw,f Insight Centre for Data Analytics May 2, 2018 Slide 26

72 Lemmas Let M be a stable matching and S its closed subset Insight Centre for Data Analytics May 2, 2018 Slide 27

73 Lemmas Let M be a stable matching and S its closed subset Let w i, f j be a stable pair Insight Centre for Data Analytics May 2, 2018 Slide 27

74 Lemmas Let M be a stable matching and S its closed subset Let w i, f j be a stable pair 1. If w i, f j M 0, then w i, f j M iff ρ ei,j / S. Insight Centre for Data Analytics May 2, 2018 Slide 27

75 Lemmas Let M be a stable matching and S its closed subset Let w i, f j be a stable pair 1. If w i, f j M 0, then w i, f j M iff ρ ei,j / S. 2. Else, if w i, f j M z, then w i, f j M iff ρ pi,j S. Insight Centre for Data Analytics May 2, 2018 Slide 27

76 Lemmas Let M be a stable matching and S its closed subset Let w i, f j be a stable pair 1. If w i, f j M 0, then w i, f j M iff ρ ei,j / S. 2. Else, if w i, f j M z, then w i, f j M iff ρ pi,j S. 3. Otherwise, w i, f j M iff ρ pi,j S ρ ei,j / S. Insight Centre for Data Analytics May 2, 2018 Slide 27

77 Rotation-based (SAT) Formulation Insight Centre for Data Analytics May 2, 2018 Slide 28

78 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Insight Centre for Data Analytics May 2, 2018 Slide 28

79 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 Insight Centre for Data Analytics May 2, 2018 Slide 28

80 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : Insight Centre for Data Analytics May 2, 2018 Slide 28

81 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j Insight Centre for Data Analytics May 2, 2018 Slide 28

82 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j 2. Else if w i, f j NSP : x i,j Insight Centre for Data Analytics May 2, 2018 Slide 28

83 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j 2. Else if w i, f j NSP : x i,j 3. Else if w i, f j M 0, then x i,j == r ei,j Insight Centre for Data Analytics May 2, 2018 Slide 28

84 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j 2. Else if w i, f j NSP : x i,j 3. Else if w i, f j M 0, then x i,j == r ei,j 4. Else, if w i, f j M z, then x i,j == r pi,j Insight Centre for Data Analytics May 2, 2018 Slide 28

85 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j 2. Else if w i, f j NSP : x i,j 3. Else if w i, f j M 0, then x i,j == r ei,j 4. Else, if w i, f j M z, then x i,j == r pi,j 5. Otherwise, x i,j == r pi,j r ei,j Insight Centre for Data Analytics May 2, 2018 Slide 28

86 Rotation-based (SAT) Formulation Variables A Boolean variable x i,j for every pair w i, f j A Boolean variable r k for every rotation ρ k Constraints Closed Subset: ρ 1 ρ 2 : r 2 = r 1 w i, f j : 1. if w i, f j FP : x i,j 2. Else if w i, f j NSP : x i,j 3. Else if w i, f j M 0, then x i,j == r ei,j 4. Else, if w i, f j M z, then x i,j == r pi,j 5. Otherwise, x i,j == r pi,j r ei,j Easily translated in SAT (Γ) Insight Centre for Data Analytics May 2, 2018 Slide 28

87 Important Properties of the SAT Formula Insight Centre for Data Analytics May 2, 2018 Slide 29

88 Important Properties of the SAT Formula Let M2M(I, X (M2M)) be the stable matching constraint Insight Centre for Data Analytics May 2, 2018 Slide 29

89 Important Properties of the SAT Formula Let M2M(I, X (M2M)) be the stable matching constraint Unit propagation on Γ does not maintain arc consistency Insight Centre for Data Analytics May 2, 2018 Slide 29

90 Important Properties of the SAT Formula Let M2M(I, X (M2M)) be the stable matching constraint Unit propagation on Γ does not maintain arc consistency Theorem: Let D be a domain such that unit propagation is performed without failure on Γ. There exists at least a solution in D that satisfies Γ. Insight Centre for Data Analytics May 2, 2018 Slide 29

91 Arc Consistency Insight Centre for Data Analytics May 2, 2018 Slide 30

92 Arc Consistency Arc Consistency Idea: use unit propagation as a support check Some assignments already have supports O(L 2 ) time Insight Centre for Data Analytics May 2, 2018 Slide 30

93 Experimental Protocol Insight Centre for Data Analytics May 2, 2018 Slide 31

94 Experimental Protocol Models: fr: SAT-formula ac: Arc Consistency bc: State-of-the art propagator [16-stability] Insight Centre for Data Analytics May 2, 2018 Slide 31

95 Experimental Protocol Models: fr: SAT-formula ac: Arc Consistency bc: State-of-the art propagator [16-stability] Lexicographical branching (random, min-max random), activity-based search, impact-based search Insight Centre for Data Analytics May 2, 2018 Slide 31

96 Experimental Protocol Models: fr: SAT-formula ac: Arc Consistency bc: State-of-the art propagator [16-stability] Lexicographical branching (random, min-max random), activity-based search, impact-based search Insight Centre for Data Analytics May 2, 2018 Slide 31

97 Experimental Protocol Models: fr: SAT-formula ac: Arc Consistency bc: State-of-the art propagator [16-stability] Lexicographical branching (random, min-max random), activity-based search, impact-based search Sex-Equal/Balanced Stable matching Insight Centre for Data Analytics May 2, 2018 Slide 31

98 Sex-Equal Stable Matching: Optimality Evaluation CPU Time bc-isbc-asbc-lx-mn bc-lx-rd fr-isfr-asfr-lx-mn fr-lx-rd ac-isac-asac-lx-mn ac-lx-rd Optimality ratio Insight Centre for Data Analytics May 2, 2018 Slide 32

99 Sex-Equal Stable Matching: Optimality Evaluation CPU Time bc-isbc-asbc-lx-mn bc-lx-rd fr-isfr-asfr-lx-mn fr-lx-rd ac-isac-asac-lx-mn ac-lx-rd Optimality ratio Clear dominance of the SAT formulation Arc Consistency does not pay off Insight Centre for Data Analytics May 2, 2018 Slide 32

100 Sex-Equal Stable Matching: Quality of The Solution CPU Time bc-isbc-asbc-lx-mn bc-lx-rd fr-isfr-asfr-lx-mn fr-lx-rd ac-isac-asac-lx-mn ac-lx-rd Objective ratio Insight Centre for Data Analytics May 2, 2018 Slide 33

101 Conclusions & Future Research Insight Centre for Data Analytics May 2, 2018 Slide 34

102 Conclusions & Future Research Contributions Robust solutions Modularity & Flexibility of CP to solve hard problems Insight Centre for Data Analytics May 2, 2018 Slide 34

103 Conclusions & Future Research Contributions Robust solutions Modularity & Flexibility of CP to solve hard problems Future Research Other stable matching Problems? E.g., preferences including ties? and 3D stable matching? From (1,b)-supermatch to (a,b)-supermatch? Algorithmic complexity study for robust solutions? Insight Centre for Data Analytics May 2, 2018 Slide 34

104 Insight Centre for Data Analytics May 2, 2018 Slide 35

105 References I Emmanuel Hebrard. Robust solutions for constraint satisfaction and optimisation under uncertainty. PhD thesis, University of New South Wales, Vipul Bansal, Aseem Agrawal, and Varun S. Malhotra. Polynomial time algorithm for an optimal stable assignment with multiple partners. Theor. Comput. Sci., 379(3): , Mohamed Siala and Barry O Sullivan. Revisiting two-sided stability constraints. In Integration of AI and OR Techniques in Constraint Programming - 13th International Conference, CPAIOR 2016, Banff, AB, Canada, May 29 - June 1, 2016, Proceedings, pages , Dan Gusfield and Robert W. Irving. The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge, MA, USA, Insight Centre for Data Analytics May 2, 2018 Slide 36

106 References II Begum Genc, Mohamed Siala, Gilles Simonin, and Barry O Sullivan. On the complexity of robust stable marriage. In Combinatorial Optimization and Applications - 11th International Conference, COCOA 2017, Shanghai, China, December 16-18, 2017, Proceedings, Part II, pages , Mohamed Siala, Emmanuel Hebrard, and Marie-José Huguet. An optimal arc consistency algorithm for a chain of atmost constraints with cardinality. In Principles and Practice of Constraint Programming - 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, Proceedings, pages 55 69, Mohamed Siala, Christian Artigues, and Emmanuel Hebrard. Two clause learning approaches for disjunctive scheduling. In Principles and Practice of Constraint Programming - 21st International Conference, CP 2015, Cork, Ireland, August 31 - September 4, 2015, Proceedings, pages , Insight Centre for Data Analytics May 2, 2018 Slide 37

107 References III Mohamed Siala and Barry O Sullivan. Rotation-based formulation for stable matching. In Principles and Practice of Constraint Programming - 23rd International Conference, CP 2017, Melbourne, VIC, Australia, August 28 - September 1, 2017, Proceedings, pages , Christian Artigues, Emmanuel Hebrard, Valentin Mayer-Eichberger, Mohamed Siala, and Toby Walsh. SAT and hybrid models of the car sequencing problem. In Integration of AI and OR Techniques in Constraint Programming - 11th International Conference, CPAIOR 2014, Cork, Ireland, May 19-23, Proceedings, pages , Mohamed Siala and Barry O Sullivan. Revisiting two-sided stability constraints. In Integration of AI and OR Techniques in Constraint Programming - 13th International Conference, CPAIOR 2016, Banff, AB, Canada, May 29 - June 1, 2016, Proceedings, pages , Insight Centre for Data Analytics May 2, 2018 Slide 38

108 References IV Emmanuel Hebrard and Mohamed Siala. Explanation-based weighted degree. In Integration of AI and OR Techniques in Constraint Programming - 14th International Conference, CPAIOR 2017, Padua, Italy, June 5-8, 2017, Proceedings, pages , Guillaume Escamocher, Mohamed Siala, and Barry O Sullivan. From backdoor key to backdoor completability: Improving a known measure of hardness for the satisfiable csp. In Integration of AI and OR Techniques in Constraint Programming - 15th International Conference, CPAIOR June 2018, Delft, The Netherlands., Mohamed Siala, Emmanuel Hebrard, and Marie-José Huguet. An optimal arc consistency algorithm for a particular case of sequence constraint. Constraints, 19(1):30 56, Nina Narodytska, Thierry Petit, Mohamed Siala, and Toby Walsh. Three generalizations of the FOCUS constraint. Constraints, 21(4): , Insight Centre for Data Analytics May 2, 2018 Slide 39

109 References V Mohamed Siala, Emmanuel Hebrard, and Marie-José Huguet. A study of constraint programming heuristics for the car-sequencing problem. Engineering Applications of Artificial Intelligence, 38:34 44, Matthew L. Ginsberg, Andrew J. Parkes, and Amitabha Roy. Supermodels and robustness. In In AAAI/IAAI, pages , Danuta Sorina Chisca, Mohamed Siala, Gilles Simonin, and Barry O Sullivan. New models for two variants of popular matching. In 29th IEEE International Conference on Tools with Artificial Intelligence (ICATI) November 2017, Boston, Massachussets, USA. Nina Narodytska, Thierry Petit, Mohamed Siala, and Toby Walsh. Three generalizations of the FOCUS constraint. In IJCAI 2013, Proceedings of the 23rd International Joint Conference on Artificial Intelligence, Beijing, China, August 3-9, 2013, pages , Begum Genc, Mohamed Siala, Barry O Sullivan, and Gilles Simonin. Finding robust solutions to stable marriage. In Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, Melbourne, Australia, August 19-25, 2017, pages , Insight Centre for Data Analytics May 2, 2018 Slide 40