Complexity and Approximability of the Mamlming Probhem.

Let G. e. a digraph wihl cosicive eCge weighns as whlS as s and e be two veetic5s of G. The aai'lang nroblea (MP(stetes Ilow to aark -osa- cdgc-oe G wit h T and F, wliere every nnUi -torhinh; el sourni s will reae2laig8d il and the totol raiig- if the mnli-d edgns is aiaiaal. Wli-n Inadersing elii diea'ahle 7'-marked edges alioa-d re followed while F-aarded ednes should nnt. The basia a-nliia-idns and properties of the marking prols ge ne havn Igiee mvesteted i n [1]. This piapid diovidoe new cnntefouUons 13 td. a3-nng prablaa: as follows: (i- tho MP is NP-Complete own if the imde-lving digteph is an unweighted pinpry DAG; (It-the MP rannae ag a2lirrximaeed whhin tilean iw an anwelgytcd DAG and sven in an anweighted 'inary DAG with n vertices, where a is a constant. Moreover, a lower 'oand to the optimal solatisn of tDe IMF1 ie provide.. We also stud(tte eompleth v and ttal- lenges of the aaraing proMea in program flow graphs. [ABSTRACT FROM AUTHOR]