This paper presents a state-based scheduling algorithm for the selection of the next logical process (LP) to be run on a processor in a Time Warp synchronized parallel discrete event simulation. In our solution, state information related to the LPs in the immediate predecessor set of a given LP is used to compute its scheduling priority. This distances our algorithm from previous solutions where the scheduling priority is assigned basing exclusively on local state information related to the LPs sharing the processor.As a system to spread the required state information, we use a classical piggybacking technique (i.e. state information is attached to any message carrying a simulation event/anti-event). This solution adds negligible overhead but does not prevent state information from becoming stale. To tackle staleness we introduce a notion of information filtering and present an iterative procedure for the selection of an adequate value for the filter length that determines both the amount of (and also what) state information is actually relevant for computing the priority of any LP.An empirical study of a classical benchmark is reported for a comparison with the Lowest-Timestamp-First algorithm. The obtained data point out the effectiveness of our algorithm in the reduction of the amount of rollback, which, in turn, leads to faster execution of the simulation.