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Four Tales Overview of Selected Research Conducted at the Constraint Systems Laboratory

Four Tales Overview of Selected Research Conducted at the Constraint Systems Laboratory Berthe Y. Choueiry Constraint Systems Laboratory Department of Computer Science & Engineering University of Nebraska-Lincoln. The projects. GTAAP (Lim, Guddeti, Thota, Zou)

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Four Tales Overview of Selected Research Conducted at the Constraint Systems Laboratory

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  1. Four Tales Overview of Selected Research Conducted at the Constraint Systems Laboratory Berthe Y. Choueiry Constraint Systems Laboratory Department of Computer Science & Engineering University of Nebraska-Lincoln 4C Visit—Choueiry

  2. The projects • GTAAP (Lim, Guddeti, Thota, Zou) • Temporal Reasoning (Xu, Shi) • Interchangeability (Beckwith-Davis, Lal, Freuder) • Structural decompositions (Zheng, Gompert) Funding: NSF CAREER, ERP/NSF-EPSCoR, NASA Nebraska Space Grant, Fling Fellowship, Layman Award, CSE. 4C Visit—Choueiry

  3. GTAAP • Given • A set of academic tasks • A set of GTAs to assign to these tasks • A set constraints restricting combinations • Find a consistent & satisfactory assignment • Consistent: assignment breaks no (hard) constraints • Satisfactory: assignment maximizes • number of courses covered • happiness of the GTAs 4C Visit—Choueiry

  4. Motivation • Context • “Most difficult duty of a department chair” [Reichenbach, 2000] • Assignments done manually, countless reviews, persistent inconsistencies • Unhappy instructors, unhappy GTAs, unhappy students • Observation • Computers are good at maintaining consistency • Humans are good at balancing tradeoffs • Our solution • An online, constraint-based system • With interactive & automated search mechanisms 4C Visit—Choueiry

  5. System architecture Server Environment (cse.unl.edu) Client Student Web-interface Univ Databases Profile Information Course Information Student Database (GTAs & Courses) Manager Web-interface Hire GTAs Setup courses Interactive Search Interactive selections Interactive Solver Manager Automated Search Heuristic BT LS ERA Randomized BT 4C Visit—Choueiry

  6. Manager interface: Interactive Selection 4C Visit—Choueiry

  7. Dual perspective Task-centered view Resource-centered view 4C Visit—Choueiry

  8. Problem solving • Interactive decision making • Seamlessly switching between perspectives • Propagates decisions (MAC) • Automated search algorithms • Heuristic backtrack search (BT) • Stochastic local search (LS) • Multi-agent search (ERA) • Randomized backtrack search (RDGR) • Future: Cooperative/hybrid strategies • Extensions: Auction-based, GA, MIP, LD-search, etc. 4C Visit—Choueiry

  9. Comparing solvers • Using the same CSP encoding, students implements solvers separately and competed for best results • Experience lead to the identification of behavioral criteria and regimes that characterize the performance of the various solvers in the context of GTAP • Criteria: Stability, solution length, vulnerability to local optima, deadlock, thrashing, etc. 4C Visit—Choueiry

  10. GTAAP: conclusions • Integrated interactive & automated problem-solving strategies • Reduced the burden of the manager • Lead to quick development of ‘stable’ solutions • Our efforts • Helped the department • Trained students in CP techniques • Paved new avenues for research • Cooperative, hybrid search • Visualization of solution space 4C Visit—Choueiry

  11. Projects • GTAAP (Lim, Guddeti, Thota, Zou) • Temporal Reasoning (Xu, Shi) • Interchangeability (Beckwith-Davis, Lal, Freuder) • Structural decompositions (Zheng, Gompert) Funding: NSF CAREER, ERP/NSF-EPSCoR,NASA Nebraska Space Grant, Fling Fellowship, Layman Award, CSE. 4C Visit—Choueiry

  12. Temporal networks • Simple Temporal Problem • Floyd-Warshall, Bellman-Ford • STP [Time 03, AAAI 04] • Temporal Constraint Satisfaction Problem • Search + ULT [Schwalb & Dechter 97] • AC, EdgeOrd, NewCycle[AI Comm 04,CP 03] • Disjunctive Temporal Problem • Search + heuristics [S&K 00, O&C 00, Tsa&P 03] • Some of our results are applicable 4C Visit—Choueiry

  13. AC Single n-ary constraint GAC is NP-hard AC Works on existing triangles Poly # of poly constraints Preprocessing the TCSP 4C Visit—Choueiry

  14. Advantages of AC • Uses data structures similar to AC-4 • May be optimal 4C Visit—Choueiry

  15. TCSP as a meta-CSP • Use STP to solve individual STPs efficiently • Especially effective on sparse networks 4C Visit—Choueiry

  16. Algorithms for the STP Temporal graph F-W PPC STP • PPC for solving the STP improved [Bliek & Sam-Haroud 99] • Simultaneously update all edges in a triangle • STP is a refinement of PPC,considers the network as composed by triangles instead of edges FW(+AP) < BF(+AP) < incBF(+AP) < DPC(+AP) < STP 4C Visit—Choueiry

  17. Heuristics: EdgeOrd & NewCycle • Check presence of new cycles O(|E|) • Check consistency (STP) only in a cycle is added to the graph 4C Visit—Choueiry

  18. Cumulative improvement Before, after AP, after NewCyc,… … and now (AC, STP, NewCyc, EdgeOrd) Max on y-axis 18.000, 2 orders of magnitude improvement Max on y-axis 5.000.000 4C Visit—Choueiry

  19. Projects • GTAAP (Lim, Guddeti, Thota, Zou) • Temporal Reasoning (Xu, Shi) • Interchangeability (Beckwith-Davis, Lal, Freuder) • Structural decompositions (Zheng, Gompert) Funding: NSF CAREER, ERP/NSF-EPSCoR, NASA Nebraska Space Grant,Fling Fellowship, Layman Award, CSE. 4C Visit—Choueiry

  20. {c, d, e, f } V2 {d} V1 V4 {a, b, d} {a, b, c} Value interchangeability [Freuder 91] Equivalent values in the domain of a variable V3 • Full Interchangeability (FI): • d, e, f interchangeable for V2 in any solution • Neighborhood Interchangeability (NI): • Efficiently approximates FI • Finds e,f but misses d • Discrimination tree DT(Vx) 4C Visit—Choueiry

  21. V1 V2 { c, d, e, f } {d} S S S V1 V1 V1 d d d V4 V3 V2 V2 V2 {a, b, d} {a, b, c} c e f d c e, f d c d, e, f Bundling: using NI in search Static bundling Dynamic bundling BT • Static bundling [Haselböck, 93] • Dynamic bundling • Re-computes NI during search • Objection: Costly & not worthwhile 4C Visit—Choueiry

  22. V {3, 4} {1, 2} V1 {1, 3} {1} {1} V2 {3} V3 {2} No-good bundle {1} V4 Solution bundle Bundling vs dynamic bundling DynBndl • Can be done at no more cost than FC • Yields larger bundles • Boosts benefits of bundling • Bundles solutions • Bundles no-goods 4C Visit—Choueiry

  23. Contributions • Generalized NI to non-binary CSPs • Showed how to use DT (nb-DT) for forward checking • Conducted empirical evaluations • Varying tightness, domain size, etc. • Measuring: • FBS, size of the first solution bundle • NV, number of nodes visited in the search tree • CC, number of constraints checked • CPU time 4C Visit—Choueiry

  24. FC 20 n=20 t FBS 0.350 33.44 a=15 18 Time [sec] DynBndl 0.400 10.91 CR=CR3 16 #NV, hundreds 0.425 7.13 0.437 6.38 14 0.450 5.62 12 0.462 2.37 FC 0.4750.66 10 0.500 0.03 NV 8 0.550 0.00 6 DynBndl 4 2 CPU time 0 0.325 0.35 0.375 0.4 0.425 0.45 0.475 0.5 0.525 0.55 0.575 0.6 Tightness Analysis: varying tightness • Low tightness • Large FBS • 33 at t=0.35 • 2254 (Dataset #13, t=0.35) • Small additional cost • Phase transition • Multiple solutions present • Maximum no-good bundling causes max savings in CPU time, NV, & CC • High tightness • Problems mostly unsolvable • Overhead of bundling minimal 4C Visit—Choueiry

  25. Analysis: Varying domain size • Increasing a in phase-transition • FBS increases: More chances for symmetry • CPU time decreases: more bundling of no-goods Increasing a (n=30) Because the benefits of DynBndl increase with increasing domain size, DynBndl is particularly interesting for database applications where large domains are typical 4C Visit—Choueiry

  26. The join query Join query • SELECT R2.A,R2.B,R2.C • FROM R1,R2 • WHERE R1.A=R2.A • AND R1.B=R2.B • AND R1.C=R2.C (Compacted) R1 R2 Result: 10 tuples in 3 nested tuples A B C {1, 5} {12, 13, 14} {23} {2, 4} {10} {25} {6} {13, 14} {27} 4C Visit—Choueiry

  27. R1.A R1.B R1.C R2 R1 R2.C R2.A R2.B Modeling join query as a CSP • Attributes of relations  CSP variables • Attribute values  variable domains • Relations  relational constraints • Join conditions  join-condition constraints • SELECT R1.A,R1.B,R1.C • FROM R1,R2 • WHERE R1.A=R2.A • AND R1.B=R2.B • AND R1.C=R2.C 4C Visit—Choueiry

  28. Bundling-based join computation • Progressive Merge-Join (PMJ): a sort-merge algorithm by [Dittrich et al. ‘03] • Two phases • Sorting: sorts sub-sets of relations & produces early results • Merging phase: merges sorted sub-sets • Implementation & evaluationon XXL library • Compaction rate achieved (even with preliminary implementation) • Random problem: 1.48 • Real-world problem: 2.26 (69 tuples in 32 nested tuples) 4C Visit—Choueiry

  29. Projects • GTAAP (Lim, Guddeti, Thota, Zou) • Temporal Reasoning (Xu, Shi) • Interchangeability (Beckwith-Davis, Lal, Freuder) • Structural decompositions (Zheng, Gompert) Funding: NSF CAREER, ERP/NSF-EPSCoR, NASA Nebraska Space Grant, Fling Fellowship, Layman Award, CSE. 4C Visit—Choueiry

  30. Structural decomposition methods HYPERTREE Gottlob et al., 2002 HYPERCUTSET Gottlob et al., 2000 HINGETCLUSTER Gyssens et al., 1994 HINGE+ CaT TRAVERSE TCLUSTER Dechter & Pearl, 1989 HINGE Gyssens et al., 1994 CUT CUTSET Dechter, 1987 BICOMP Freuder, 1985 Criteria for comparing decomposition methods: • Width of an x-decomposition = largest number of hyperedges in a node of the tree generated by x-decomposition • CPU time for generating the tree 4C Visit—Choueiry

  31. Results on random CSPs • CPU time: • Width: TRAVERSE HINGE CUT CaT  HINGE+ HYPERTREE    HYPERTREE  CaT HINGE+ CUT HINGE TRAVERSE   4C Visit—Choueiry

  32. IndSet + local search • Decomposition using independent sets • Integration with local search • Refinement with dangle identification 4C Visit—Choueiry

  33. IndSet: decompose Decompose CSP into Ī & I • We find IndSet using the polynomial-time CliqueRemoval algorithm [Boppana & Halldórsson, ‘90] 4C Visit—Choueiry

  34. IndSet: solve Solve Ī, using any technique 4C Visit—Choueiry

  35. IndSet: propagate Apply DAC: Revise(I, Ī) If no domain in I is empty, we have • solved the original CSP • found multiple solutions (cross product of domains in I) 4C Visit—Choueiry

  36. SLS/IndSet • Solve Ī using SLS (with steepest descent) • 5 heuristics to account for the constraints betweenIand Ī 4C Visit—Choueiry

  37. Finding dangles • Identify T dangles • Perform DAC TI’ • Apply SLS/IndSet on C & I’ instead of on Ī & I • Extend to T, in parallel 4C Visit—Choueiry

  38. Effect of dangles • Reduces the size of the cutset • Increases the number of solutions • Slightly improves runtime • Better yet: find dangles before decomposition 4C Visit—Choueiry

  39. Recursive decomposition • RecIndSet • RecCliq: repeatedly find & remove cliques • Quality of generated pseudo trees? A Ia B Ib I I C Ic 4C Visit—Choueiry

  40. Conclusions • Past and present • GTAAP (Lim, Guddeti, Thota, Zou) • Temporal Reasoning (Xu, Shi) • Interchangeability (Beckwith-Davis, Lal, Freuder) • Structural decompositions (Zheng, Gompert) • Future • Explore new areas: software engineering, DBs, wireless communications, digital humanities • Improve visualization and user interaction • Continue with decomposition and interchangeability (same old story..) 4C Visit—Choueiry

  41. Thank you for your attention Any time left for questions? 4C Visit—Choueiry

  42. Manager interface: TA Hiring & Load 4C Visit—Choueiry

  43. GTA interface: Preference Specification 4C Visit—Choueiry

  44. Motivation (revisited) • Most difficult duty of a department chair” • Keeps the manager in the decision loop while removing the need for tedious and error-prone manual assignments • Helps producing quick (3 weeks down to 2 days) and satisfactory (stable) assignments • Initially, assignments were manually done on paper • Now, on-line data acquisition process • Enabled department to streamline & standardize GTA selection, hiring, and assignment • Overworked staff, unhappy GTAs • Overjoyed staff (relieved from handling application forms and massive paperwork) • Enthusiastic anonymous online reviews from applicants 4C Visit—Choueiry

  45. Comparisons 4C Visit—Choueiry

  46. 1. Effect of varying run time • RDGR consistently outperforms RGR • Running time does not affect the relative dominance 4C Visit—Choueiry

  47. 2. Choice ofrin RGR r = 1.1 for RGR for GTAAP & random CSPs 4C Visit—Choueiry

  48. 2. Choice of rin RDGR r = 1.1 for GTAAP r = 2 for random CSPs 4C Visit—Choueiry

  49. 3. Performance: SQDs • Under-constrained: ERA > RDGR > RGR > BT > LS • Over-constrained: RDGR > RGR > BT > LS > ERA 4C Visit—Choueiry

  50. 3. SQDs at phase transition • Solvable: ERA still wins for smallest deviations • Unsolvable: RDGR > RGR > BT > ERA > LS 4C Visit—Choueiry

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