Praise be to Allah.
It is not permissible to walk across in front of someone who is praying, and it is a great sin, as the Prophet (peace be upon him) said (approximate translation of meaning is):
"If the one crossing in front of a praying person knew what sin is upon him, it would be better for him to wait forty than walk across." Abu Al-Nadhr (one of the narrators of the hadith) said: I don't know whether he said forth days, months, or years. (Bukhari)
Imam Al-Bukhari (R) has named the chapter in which he brings the hadith as follows: Chapter on the sin of walking across in front of a praying person.
When the praying person is the leader in the prayer or praying alone, and he has a sutrah( some object like a peice of wood) in front of him, then walking across in between him and his sutrah is not permitted. However, if he is praying without a sutrah, it is not permissible to walk across in between him and his place of prostration. For the followers (in a jamaa'ah prayer), the leader's sutrah is enough for them. Based on this, it is permissible to walk through in front of a row if need be.
And Allah knows best.