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 Carpet_Cutting — Constraint detection

A formal specification of an instance I of the carpet cutting problem is defined as follows . We are given 3 sets of disjoint objects : -LRB- i -RRB- Room is a set of room carpets . Each $ c \ in Room $ is defined by a set of rectangles $ c.rect $ . For each rectangle $ r \ in c.rect $ we have a length $ r.len $ and width $ r.wid $ -LRB- in the 0-degrees orientation -RRB- together with an offset $ -LRB- r.ox , r.oy -RRB- $ from the origin of the room carpet -LRB- in the 0-degrees orientation -RRB- . Moreover , each $ c \ in Room $ is also given a set of allowable orientations $ c.ori \ subset -LCB- 0-degrees , 90-degrees , 180-degrees , 270-degrees -RCB- $ . -LRB- ii -RRB- Str is a set of stair carpets . For each $ c \ in Str $ we have a width $ c.wid $ , step length $ c.step $ and number of steps $ c.n $ as well as a maximum number of pieces $ c.pcs $ and minimum steps per piece length $ c.min $ . -LRB- iii -RRB- Edg is a set of edge filler carpets . For each $ c \ in Edg $ we have a width $ c.wid $ , length $ c.len $ as well as a maximum number of pieces $ c.pcs $ and minimum length per piece length $ c.min $ . The remaining part of the model is a set $ Pile \ subset Room $ which determines which carpets must be pile aligned , i.e. $ c.ori = -LCB- 0-degrees , 180-degrees -RCB- $ for each $ c \ in Pile $ , and a roll width RW . Hence , I = -LRB- Room , Str , Edg , Pile , RW -RRB- . Note that all stair and edge filler carpets must be pile aligned , but this constraint can be neglected , since the pile orientations are symmetrical for rectangles as it is for parts of these carpets . The aim is to find an allowable partitioning $ c.part $ of each carpet $ c \ in Str \ union Edg $ into rectangles , and position $ -LRB- x , y -RRB- $ and allowed orientation for each rectangle r appearing in a room carpet such that : none of the rectangles overlap ; each of the rectangles in a room carpet are correctly offset from the origin of the carpet ; all pile aligned carpets are aligned in the same orientation ; the roll width and length constraints are met , the minimal steps and maximal break constraints for the stair carpets are satisfied , and the roll length RL is minimised .

Problem Carpet_Cutting — Detection of the decisions and objects to be modeled

A formal specification of an instance I of the carpet cutting problem is defined as follows . We are given 3 sets of disjoint objects : -LRB- i -RRB- Room is a set of room carpets . Each $ c \ in Room $ is defined by a set of rectangles $ c.rect $ . For each rectangle $ r \ in c.rect $ we have a length $ r.len $ and width $ r.wid $ -LRB- in the 0-degrees orientation -RRB- together with an offset $ -LRB- r.ox , r.oy -RRB- $ from the origin of the room carpet -LRB- in the 0-degrees orientation -RRB- . Moreover , each $ c \ in Room $ is also given a set of allowable orientations $ c.ori \ subset -LCB- 0-degrees , 90-degrees , 180-degrees , 270-degrees -RCB- $ . -LRB- ii -RRB- Str is a set of stair carpets . For each $ c \ in Str $ we have a width $ c.wid $ , step length $ c.step $ and number of steps $ c.n $ as well as a maximum number of pieces $ c.pcs $ and minimum steps per piece length $ c.min $ . -LRB- iii -RRB- Edg is a set of edge filler carpets . For each $ c \ in Edg $ we have a width $ c.wid $ , length $ c.len $ as well as a maximum number of pieces $ c.pcs $ and minimum length per piece length $ c.min $ . The remaining part of the model is a set $ Pile \ subset Room $ which determines which carpets must be pile aligned , i.e. $ c.ori = -LCB- 0-degrees , 180-degrees -RCB- $ for each $ c \ in Pile $ , and a roll width RW . Hence , I = -LRB- Room , Str , Edg , Pile , RW -RRB- . Note that all stair and edge filler carpets must be pile aligned , but this constraint can be neglected , since the pile orientations are symmetrical for rectangles as it is for parts of these carpets . The aim is to find an allowable partitioning $ c.part $ of each carpet $ c \ in Str \ union Edg $ into rectangles , and position $ -LRB- x , y -RRB- $ and allowed orientation for each rectangle r appearing in a room carpet such that : none of the rectangles overlap ; each of the rectangles in a room carpet are correctly offset from the origin of the carpet ; all pile aligned carpets are aligned in the same orientation ; the roll width and length constraints are met , the minimal steps and maximal break constraints for the stair carpets are satisfied , and the roll length RL is minimised .

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