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 049 (Number partitioning) — Constraint detection

This problem consists in finding a partition of numbers $ 1 , \ ldots , N$ into two sets A and B such that : A and B have the same cardinality ; sum of numbers in $ A$ = sum of numbers in $ B$ ; sum of squares of numbers in $ A$ = sum of squares of numbers in $ B$ . There is no solution for $ N > 8 $ . Here is an example for $ N = 8 $ : $ A = -LRB- 1,4,6,7 -RRB- $ and $ B = -LRB- 2,3,5,8 -RRB- $ . Then from $ N > = 8 $ , there is no solution if $ N$ is not a multiple of $ 4 $ .

Problem 049 (Number partitioning) — Detection of the decisions and objects to be modeled

This problem consists in finding a partition of numbers $ 1 , \ ldots , N$ into two sets A and B such that : A and B have the same cardinality ; sum of numbers in $ A$ = sum of numbers in $ B$ ; sum of squares of numbers in $ A$ = sum of squares of numbers in $ B$ . There is no solution for $ N > 8 $ . Here is an example for $ N = 8 $ : $ A = -LRB- 1,4,6,7 -RRB- $ and $ B = -LRB- 2,3,5,8 -RRB- $ . Then from $ N > = 8 $ , there is no solution if $ N$ is not a multiple of $ 4 $ .

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