1. Exsched: Solving Constraint Satisfaction Problems with the Spreadsheet Paradigm Gopal Gupta UT Dallas & Logical Software Solutions Siddharth Chitnis, Madhu Yennamini University of Texas at Dallas

2. The Spreadsheet Paradigm Used for Manipulating Table(s) of Data Used for Manipulating Table(s) of Data Data Centered: User is always looking at the data; programming is done around the data (data-oriented prog.) Data Centered: User is always looking at the data; programming is done around the data (data-oriented prog.) Data items in each row/column have similar characteristics Data items in each row/column have similar characteristics Programming done by replication Programming done by replication Replication is parametrized: give one example of a computation, then replicate it multiple times (with appropriate transformations applied). Replication is parametrized: give one example of a computation, then replicate it multiple times (with appropriate transformations applied). No looping construct used: iterations replicated explicitly with the index variables set appropriately. No looping construct used: iterations replicated explicitly with the index variables set appropriately.

3. Spreadsheet Paradigm Man-machine interface for handling complex multi- dimensional data. Man-machine interface for handling complex multi- dimensional data. Paper and pencil approach to solving problems Paper and pencil approach to solving problems Spreadsheets: Popular for arithmetic computations Spreadsheets: Popular for arithmetic computations Current spreadsheets: limited to arithmetic Current spreadsheets: limited to arithmetic Arithmetic expressions are interactively entered and evaluated until desired results are obtained Arithmetic expressions are interactively entered and evaluated until desired results are obtained Repetitive computations are performed by copying expressions from one cell to a range of cells, with appropriate transformation applied Repetitive computations are performed by copying expressions from one cell to a range of cells, with appropriate transformation applied Question: Can we generalize these arithmetic (functional) computations (to relational)? Question: Can we generalize these arithmetic (functional) computations (to relational)?

4. Spreadsheets and CSPs: Motivation Designing schedules is a problem that arises quite frequently: Designing schedules is a problem that arises quite frequently: Class schedules Class schedules Employee schedules Employee schedules Examination schedules Examination schedules Job schedules Job schedules Degree audits for students Degree audits for students These schedules have a tabular, 2-D structure These schedules have a tabular, 2-D structure The constraints to be met are similar across rows and columns The constraints to be met are similar across rows and columns In general, many constraint satisfaction problems such as timetabling and scheduling problems, recreational puzzles can be modelled as tables of constraints In general, many constraint satisfaction problems such as timetabling and scheduling problems, recreational puzzles can be modelled as tables of constraints Use of spreadsheet paradigm for this purpose Use of spreadsheet paradigm for this purpose Goal: Design an interface that facilitates the interactive development of such tabular schedules Goal: Design an interface that facilitates the interactive development of such tabular schedules

5. CS Class Schedule

6. Spreadsheet and CSPs 2-D data-centered nature suggests use of of the spreadsheet paradigm to interactively develop these schedules 2-D data-centered nature suggests use of of the spreadsheet paradigm to interactively develop these schedules Scheduling requires constraint solving: generalize functional arithmetic expressions to relations (constraints/predicates). Scheduling requires constraint solving: generalize functional arithmetic expressions to relations (constraints/predicates). Obvious generalization: Use CLP(R) constraints Obvious generalization: Use CLP(R) constraints We go one step further: generalize spreadsheets so that finite domain constraints can also be entered in the cells We go one step further: generalize spreadsheets so that finite domain constraints can also be entered in the cells Yesterday: Knowledgesheet Yesterday: Knowledgesheet Today: Exsched, plug-in for Microsoft Excel Today: Exsched, plug-in for Microsoft Excel

7. Exsched Interface Interface similar to regular spreadsheet Interface similar to regular spreadsheet (extension of MS Excel) (extension of MS Excel) Each cell can be thought of as a variable or a place holder Each cell can be thought of as a variable or a place holder A user can enter finite domain values in a cell. These finite domain values denote the finite domain of the variable corresponding to the cell A user can enter finite domain values in a cell. These finite domain values denote the finite domain of the variable corresponding to the cell Example: [1..5] Constraints can also be entered in the cell. Constraints contain variable names (cell coordinates) and constants Constraints can also be entered in the cell. Constraints contain variable names (cell coordinates) and constants Example: B3 #= C4 + 1

8. Interface (continued) Constants can also be entered in the cell: the variable corresponding to that cell is set to the constant entered Constants can also be entered in the cell: the variable corresponding to that cell is set to the constant entered Constraints/constants/finite domains can either be entered into the current cell or via dialog boxes Constraints/constants/finite domains can either be entered into the current cell or via dialog boxes Constraints can be copied to a range of cells; appropriate transformations are applied while copying Constraints can be copied to a range of cells; appropriate transformations are applied while copying Large number of of built-ins available as clickable buttons Large number of of built-ins available as clickable buttons alldifferent, count, cumulative, element, subset alldifferent, count, cumulative, element, subset Once constraints/constants/finite domains are entered Once constraints/constants/finite domains are entered the system automatically collects them, the system automatically collects them, composes a clp(FD) program, composes a clp(FD) program, solves it using clp(FD) engine running in the background and solves it using clp(FD) engine running in the background and displays the solution. displays the solution.

9. Interface (continued) The user must enter The user must enter at least one Query Table and at least one Query Table and zero or more Auxiliary Tables zero or more Auxiliary Tables Query Table is used to compose the query Query Table is used to compose the query The query table could be as small as one cell The query table could be as small as one cell Auxiliary tables turn into facts: auxiliary tables useful in mapping non-integer domain values into integers Auxiliary tables turn into facts: auxiliary tables useful in mapping non-integer domain values into integers Computed results for the query are displayed in the query table Computed results for the query are displayed in the query table User can highlight a part of the query table, and only those cells are included in the query. User can highlight a part of the query table, and only those cells are included in the query.

10. Example: Employee schedule Scheduling managers at a store: Scheduling managers at a store: Store hours : 8 AM to 11 PM, 7 days / week Store hours : 8 AM to 11 PM, 7 days / week Each manager must work 8.5 hrs / day (includes 0.5 hrs for lunch) Each manager must work 8.5 hrs / day (includes 0.5 hrs for lunch) Each manager must work 5 days / week Each manager must work 5 days / week At least one manager must be present at any moment At least one manager must be present at any moment Managers working night shifts should not be allocated morning shift the following day Managers working night shifts should not be allocated morning shift the following day Schedule must be fair to all managers Schedule must be fair to all managers In most cases, this scheduling is done manually In most cases, this scheduling is done manually Erroneous, leads to employee dissatisfaction Erroneous, leads to employee dissatisfaction

11. Solution: Employee Schedule An Empty Table Assume that there are 5 managers Assume that there are 5 managers Each manager works 8.5 hrs per day either in Each manager works 8.5 hrs per day either in The morning shift (8:00 AM to 4:30 PM), or The morning shift (8:00 AM to 4:30 PM), or The midday shift (10:00 AM to 6:30 PM), or The midday shift (10:00 AM to 6:30 PM), or The evening shift (2:30 PM to 11:00 PM) The evening shift (2:30 PM to 11:00 PM)

12. Solution: Employee Schedule (continued) Morning, midday and evening shifts are denoted by 5, 2 and 4 respectively Morning, midday and evening shifts are denoted by 5, 2 and 4 respectively 0 is used to indicate a manager’s day off 0 is used to indicate a manager’s day off Domain of each cell: [0,2,4,5] Domain of each cell: [0,2,4,5] User enters domain in one cell, copies it to the rest User enters domain in one cell, copies it to the rest For no morning after night restriction, we enter the constraint: For no morning after night restriction, we enter the constraint: C2 != B2 + 1 (copied everywhere) At least one manager is present at any time during the day: At least one manager is present at any time during the day: member(4,[D2,D3,D4,D5,D6]), member(5,[D2,D3,D4,D5,D6]) No manager works for more than 5 days a week: No manager works for more than 5 days a week:count(0,[B2,C2,D2,E2,F2,G2,H2],=,2) Every manager has more or less same proportion of morning, midday and evening shifts: Every manager has more or less same proportion of morning, midday and evening shifts:sublist([2,4,5],[B2,C2,D2,E2,F2,G2,H2])

13. Solution: Employee Schedule (continued) Note: Cell constraints are replicated in all 35 cells, column constraints in B7 through H7 and row constraints in I2 through I6. [0,2,4,5], C2 != B2 + 1 (Cell Constraints) count(0,[B2,C2,D2,E2,F2,G2,H2],=,2), sublist([2,4,5], [B2,C2,D2,E2,F2,G2,H2]) (Row Constraints) member(4,[D2,D3,D4,D5,D6]), member(5,[D2,D3,D4,D5,D6]) (Column Constraints)

14. Solution: Employee Schedule (continued) Displaying a solution

15. Solution: Employee Schedule (continued) Displaying a solution along with a mapping of variable values

16. Example: The 3x3 Grid Puzzle Cell constraints: B3: B3+C3+D3 #= 15, B3+B4+B5 #= 15 B3: B3+C3+D3 #= 15, B3+B4+B5 #= 15 C3: C3+C4+C5 #= 15 C3: C3+C4+C5 #= 15 D3: D3+D4+D5 #= 15 D3: D3+D4+D5 #= 15 B4: B4+C4+D4 #= 15 B4: B4+C4+D4 #= 15 B5: B5+C5+D5 #= 15, B5+C4+D3 #= 15 B5: B5+C5+D5 #= 15, B5+C4+D3 #= 15 D5: B3+C4+D5 #= 15, alldiff([B3,B4,B5,C3,C4,C5,D3,D4,D5]) D5: B3+C4+D5 #= 15, alldiff([B3,B4,B5,C3,C4,C5,D3,D4,D5])

17. Solution: The 3x3 Grid Puzzle

18. Example: Cryptarithmetic Puzzles Most puzzles have such a graphical structure; for example, Zebra puzzleMost puzzles have such a graphical structure; for example, Zebra puzzle Exsched can be used for solving puzzles published in popular puzzle magazinesExsched can be used for solving puzzles published in popular puzzle magazines D2 #= (E2+E3+E4) DIV 10E5 #= (E2+E3+E4) MOD 10

19. Solving Large Problems Exsched is a man-machine interface for solving CSPs Exsched is a man-machine interface for solving CSPs Large problems can be solved interactively. Large problems can be solved interactively. Note: never look for optimal solution; a solution is enough. Note: never look for optimal solution; a solution is enough. Consider course scheduling at UT Dallas CS: 120+ courses with 50+ instructors in 9 classrooms Consider course scheduling at UT Dallas CS: 120+ courses with 50+ instructors in 9 classrooms The whole schedule cannot be generated in one shot The whole schedule cannot be generated in one shot Obtain the schedule piecemeal, while manually adjusting the choices. Obtain the schedule piecemeal, while manually adjusting the choices. Or: set instructors first, set timings next, set classroom last. Or: set instructors first, set timings next, set classroom last. If a solution is not found (or the system takes too long), relax constraints or reduce the size of the query table, until a solution is found, then gradually increase the query table If a solution is not found (or the system takes too long), relax constraints or reduce the size of the query table, until a solution is found, then gradually increase the query table Another approach: divide the query table into N pieces, solve each piece individually, then enforce global consistency manually. Another approach: divide the query table into N pieces, solve each piece individually, then enforce global consistency manually.

20. Current Work Add auxiliary tables support Add auxiliary tables support Develop conventions and add support for Develop conventions and add support for Mapping tables Mapping tables Reverse mapping tables Reverse mapping tables Add ability to hide constraints (constraint relaxation) Add ability to hide constraints (constraint relaxation) Add ability to hide rows/columns (constraint relaxation) Add ability to hide rows/columns (constraint relaxation) Add more function buttons Add more function buttons Allow individual cells to be named. Allow individual cells to be named. Support for automatic constraint relaxation?? Support for automatic constraint relaxation?? Support for Macros in CLP(FD)?? Support for Macros in CLP(FD)?? Add CLP(R) support (already part of SICStus) Add CLP(R) support (already part of SICStus) Spreadsheet for Engineering Design Spreadsheet for Engineering Design Our overarching philosophy is to provide all kinds of options to the user rather than providing problem solving strategies

21. Conclusion Advantages of the Exsched Approach: Advantages of the Exsched Approach: Flexibility Flexibility Interactivity Interactivity Non-experts can use it (Expert System Shell) Non-experts can use it (Expert System Shell) Managers are resource allocators!! Managers are resource allocators!! Standard (deficient) spreadsheets currently used (sorting fn used a lot) Standard (deficient) spreadsheets currently used (sorting fn used a lot) Domain specific knowledge can be incorporated Domain specific knowledge can be incorporated User and clp(FD) system cooperate to produce solutions User and clp(FD) system cooperate to produce solutions User can give partial solutions, the rest can be computed using ExSched User can give partial solutions, the rest can be computed using ExSched Disadvantages: Disadvantages: Works only for tabular clp(FD) programs Works only for tabular clp(FD) programs No automatic help if the system is over-constrained No automatic help if the system is over-constrained Challenges: Collecting data (e.g., preferences) Challenges: Collecting data (e.g., preferences) DEMO LATER DEMO LATER

22. References G. Gupta and S. Akhter. Knowledgesheet: A Spreadsheet Interface for Solving a Class of Constraint Satisfaction Problems. PADL 2000. Springer LNCS G. Gupta and S. Akhter. Knowledgesheet: A Spreadsheet Interface for Solving a Class of Constraint Satisfaction Problems. PADL 2000. Springer LNCS M. Yennamini. ExSched: Solving CSPs with Excel. M.S. Thesis. Dec. 2004. Univ. of Texas at Dallas M. Yennamini. ExSched: Solving CSPs with Excel. M.S. Thesis. Dec. 2004. Univ. of Texas at Dallas S. Chitnis. Next Generation ExSched. M.S. Thesis. May 2006. Forthcoming. S. Chitnis. Next Generation ExSched. M.S. Thesis. May 2006. Forthcoming.