The fractional weak discrepancy of a partially ordered set

Alan Shuchat, Randy Shull, Ann N. Trenk
2007 Discrete Applied Mathematics  
In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [J.G. Gimbel and A.N. Trenk, On the weakness of an ordered set, SIAM J. Discrete Math. 11 (1998) 655-663; P.J. Tanenbaum, A.N. Trenk, P.C. Fishburn, Linear discrepancy and weak discrepancy of partially ordered sets, ORDER 18 (2001) 201-225; A.N. Trenk, On k-weak orders: recognition and a tolerance result, Discrete Math. 181 (1998) 223-237]. The fractional weak
more » ... crepancy wd F (P ) of a poset P = (V , ≺) is the minimum nonnegative k for which there exists a function f : We formulate the fractional weak discrepancy problem as a linear program and show how its solution can also be used to calculate the (integral) weak discrepancy. We interpret the dual linear program as a circulation problem in a related directed graph and use this to give a structural characterization of the fractional weak discrepancy of a poset.
doi:10.1016/j.dam.2007.05.032 fatcat:7qxkvd7bobhiho4baeivwywiga