Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem 011 (ACC Basketball Scheduling) — Constraint detection

The double round-robin scheme determines that every team i plays against every other team exactly twice during the competition , once at the place of team i -LRB- a home match for i -RRB- and once at the other team 's place -LRB- an away match for i -RRB- . The first of the two matches is called the first leg ; the second is the return match . A temporally dense double round robin -LRB- DDRR -RRB- for n teams distributes the n -LRB- n-1 -RRB- matches over a minimal number of dates such that every team plays at most one match per date . When n is even , the number of dates is 2 -LRB- n-1 -RRB- . A DDRR with an odd number of teams consists of 2n dates , in each of which n-1 teams play and one team does not . This team is said to have a bye . The ACC 1997/1998 schedule in male basketball described by Nemhauser and Trick -LRB- 1998 -RRB- was a DDRR consisting of nine teams : Clemson -LRB- abbreviation Clem ; team 1 -RRB- , Duke -LRB- Duke ; 2 -RRB- , Florida State -LRB- FSU ; 3 -RRB- , Georgia Tech -LRB- GT ; 4 -RRB- , Maryland -LRB- UMD ; 5 -RRB- , North Carolina -LRB- UNC ; 6 -RRB- , North Carolina State -LRB- NCSt ; 7 -RRB- , Virginia -LRB- UVA ; 8 -RRB- , and Wake Forest -LRB- Wake ; 9 -RRB- . The problem was to find a DDRR timetable whose 18 dates are distributed over the period of 9 weeks starting December 31 , 1997 -LRB- date 1 , a Wednesday -RRB- and ending March 1 , 1998 -LRB- date 18 , a Sunday -RRB- such that there is one weekday date and one weekend date per week , subject to a number of criteria . For the purpose of comparison , only the criteria that are used by Nemhauser and Trick -LRB- 1998 -RRB- and Trick -LRB- 1998 -RRB- are considered here . Criterion 1 . Mirroring . The dates are grouped into pairs -LRB- r1 , r2 -RRB- , such that each team will get to play against the same team in dates r1 and r2 . Such a grouping is called a mirroring scheme . Nemhauser and Trick fix the mirroring scheme to : $ m = \ -LCB- -LRB- 1,8 -RRB- , -LRB- 2,9 -RRB- , -LRB- 3,12 -RRB- , -LRB- 4,13 -RRB- , -LRB- 5,14 -RRB- , -LRB- 6,15 -RRB- , -LRB- 7,16 -RRB- , -LRB- 10,17 -RRB- , -LRB- 11,18 -RRB- \ -RCB- $ to cater to one of the idiosyncratic criteria -LRB- see Criterion 9 below -RRB- . To ease the comparison with their work , this mirroring is used throughout this paper . Criterion 2 . No Two Final Aways . No team can play away on both last dates . Criterion 3 Home/Away/Bye Pattern Criterion . No team may have more than two away matches in a row . No team may have more than two home matches in a row . No team may have more than three away matches or byes in a row . No team may have more than four home matches or byes in a row . Criterion 4 Weekend Pattern . Of the weekends , each team plays four at home , four away , and one bye . Criterion 5 . First Weekends . Each team must have home matches or byes at least on two of the first five weekends . Criterion 6 . Rival Matches . Every team except FSU has a traditional rival . The rival pairs are Clem-GT , Duke-UNC , UMD-UVA , and NCSt-Wake . In the last date , every team except FSU plays against its rival , unless it plays against FSU or has a bye . Criterion 7 . Popular Matches in February . The following pairings must occur at least once in dates 11 to 18 : Duke-GT , Duke - Wake , GT-UNC , UNC-Wake . Criterion 8 . Opponent Sequence Criterion . No team plays in two consecutive dates away against Duke and UNC . No team plays in three consecutive dates against Duke , UNC , and Wake -LRB- independent of home/away -RRB- . Criterion 9 . Idiosyncratic Criterion . UNC plays its rival Duke in the last date and in date 11 . UNC plays Clem in the second date . Duke has a bye in date 16 . Wake does not play home in date 17 . Wake has a bye in the first date . Clem , Duke , UMD , and Wake do not play away in the last date . Clem , FSU , GT , and Wake do not play away in the first date . Neither FSU nor NCSt have a bye in last date . UNC does not have a bye in the first date . Among all solutions that fulfill these criteria , Nemhauser and Trick chose those solutions that suitably satisfy a number of further preferences for final selection by the ACC . These preferences and the resulting postprocessing are beyond the scope of this work .

Problem 011 (ACC Basketball Scheduling) — Detection of the decisions and objects to be modeled

The double round-robin scheme determines that every team i plays against every other team exactly twice during the competition , once at the place of team i -LRB- a home match for i -RRB- and once at the other team 's place -LRB- an away match for i -RRB- . The first of the two matches is called the first leg ; the second is the return match . A temporally dense double round robin -LRB- DDRR -RRB- for n teams distributes the n -LRB- n-1 -RRB- matches over a minimal number of dates such that every team plays at most one match per date . When n is even , the number of dates is 2 -LRB- n-1 -RRB- . A DDRR with an odd number of teams consists of 2n dates , in each of which n-1 teams play and one team does not . This team is said to have a bye . The ACC 1997/1998 schedule in male basketball described by Nemhauser and Trick -LRB- 1998 -RRB- was a DDRR consisting of nine teams : Clemson -LRB- abbreviation Clem ; team 1 -RRB- , Duke -LRB- Duke ; 2 -RRB- , Florida State -LRB- FSU ; 3 -RRB- , Georgia Tech -LRB- GT ; 4 -RRB- , Maryland -LRB- UMD ; 5 -RRB- , North Carolina -LRB- UNC ; 6 -RRB- , North Carolina State -LRB- NCSt ; 7 -RRB- , Virginia -LRB- UVA ; 8 -RRB- , and Wake Forest -LRB- Wake ; 9 -RRB- . The problem was to find a DDRR timetable whose 18 dates are distributed over the period of 9 weeks starting December 31 , 1997 -LRB- date 1 , a Wednesday -RRB- and ending March 1 , 1998 -LRB- date 18 , a Sunday -RRB- such that there is one weekday date and one weekend date per week , subject to a number of criteria . For the purpose of comparison , only the criteria that are used by Nemhauser and Trick -LRB- 1998 -RRB- and Trick -LRB- 1998 -RRB- are considered here . Criterion 1 . Mirroring . The dates are grouped into pairs -LRB- r1 , r2 -RRB- , such that each team will get to play against the same team in dates r1 and r2 . Such a grouping is called a mirroring scheme . Nemhauser and Trick fix the mirroring scheme to : $ m = \ -LCB- -LRB- 1,8 -RRB- , -LRB- 2,9 -RRB- , -LRB- 3,12 -RRB- , -LRB- 4,13 -RRB- , -LRB- 5,14 -RRB- , -LRB- 6,15 -RRB- , -LRB- 7,16 -RRB- , -LRB- 10,17 -RRB- , -LRB- 11,18 -RRB- \ -RCB- $ to cater to one of the idiosyncratic criteria -LRB- see Criterion 9 below -RRB- . To ease the comparison with their work , this mirroring is used throughout this paper . Criterion 2 . No Two Final Aways . No team can play away on both last dates . Criterion 3 Home/Away/Bye Pattern Criterion . No team may have more than two away matches in a row . No team may have more than two home matches in a row . No team may have more than three away matches or byes in a row . No team may have more than four home matches or byes in a row . Criterion 4 Weekend Pattern . Of the weekends , each team plays four at home , four away , and one bye . Criterion 5 . First Weekends . Each team must have home matches or byes at least on two of the first five weekends . Criterion 6 . Rival Matches . Every team except FSU has a traditional rival . The rival pairs are Clem-GT , Duke-UNC , UMD-UVA , and NCSt-Wake . In the last date , every team except FSU plays against its rival , unless it plays against FSU or has a bye . Criterion 7 . Popular Matches in February . The following pairings must occur at least once in dates 11 to 18 : Duke-GT , Duke - Wake , GT-UNC , UNC-Wake . Criterion 8 . Opponent Sequence Criterion . No team plays in two consecutive dates away against Duke and UNC . No team plays in three consecutive dates against Duke , UNC , and Wake -LRB- independent of home/away -RRB- . Criterion 9 . Idiosyncratic Criterion . UNC plays its rival Duke in the last date and in date 11 . UNC plays Clem in the second date . Duke has a bye in date 16 . Wake does not play home in date 17 . Wake has a bye in the first date . Clem , Duke , UMD , and Wake do not play away in the last date . Clem , FSU , GT , and Wake do not play away in the first date . Neither FSU nor NCSt have a bye in last date . UNC does not have a bye in the first date . Among all solutions that fulfill these criteria , Nemhauser and Trick chose those solutions that suitably satisfy a number of further preferences for final selection by the ACC . These preferences and the resulting postprocessing are beyond the scope of this work .

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