Parameterized resiliency problems

Solving the Workflow Satisfiability Problem using General Purpose Solvers

“…The WSP in all its generality is a problem with complicated constraints which may require a certain partial order in which the steps are performed, exclusion of certain steps from being performed by a plan under certain conditions, etc., see e.g. [5], [6], [7], [8]. However, it is possible to reduce such a general WSP to a number of more basic WSPs in which there are no constraints imposing a partial order of the steps (i.e.…”

“…the order in which the steps are performed is immaterial), no steps are excluded from being performed, etc., see e.g. [6], [7]. Because of the reductions and since new WSP notions introduced in this paper are already of interest for the basic WSP, we will restrict our attention to the basic WSP (an instance of such a WSP is depicted in Figure 1) which is described above and formally defined in Section 3.…”

“…In fact, the time O * (2 k log k ) is highly likely to be optimal: Cohen et al [14] proved that unless the Exponential Time Hypothesis (ETH) fails, there is no algorithm of running time O * (2 o(k log k) ) for the WSP with UI constraints; Gutin and Wahlström [22] showed that unless the Strong ETH fails, there is no algorithm of running time O * (c k log k ) for any constant c < 2 for the WSP with UI constraints only. 7 6. All logarithms in this paper are of base 2.…”

High-Multiplicity Fair Allocation Using Parametric Integer Linear Programming

“…Eisenbrand and Shmonin [16,Theorem 4.2] gave an algorithm that, if the number of variables is fixed, solves the given instance of Parametric ILP (PILP) in polynomial time. To the best of our knowledge, Crampton et al [15,Corollary 2.2] were the first to give an "interpretation" of the result of Eisenbrand and Shmonin [16] in terms of parameterized complexity analysis. More specifically, they showed membership in the complexity class FPT, that is, they showed a running time f (p, n)•|I| for an instance I of PILP provided that the coefficients of the matrix A are encoded in unary.…”

“…More specifically, they showed membership in the complexity class FPT, that is, they showed a running time f (p, n)•|I| for an instance I of PILP provided that the coefficients of the matrix A are encoded in unary. Using this result Crampton et al [15] initiated the parameterized study of the so-called resiliency problems (such as the Resiliency Closest String problem).…”