Approximate algorithms for time separation of events

Abstract

We describe a polynomial-time approximate algorithm for computing minimum and maximum time separations between all pairs of events in systems specijied by acyclic timing constraint graphs. Even for acyclic graphs, the problem is NP-complete. We propose finding an approximate solution by first approximating the non-convex feasible space with a suitable convex "envelope", and then solving the problem ejjiciently in the approximate convex space. Unlike previous works, our algorithm can handle both min and m a type timing constraints in the same system, and has a computational complexity that is polynomial in the number of events. Although the computed separations are conservative in the worst-case, experiments indicate that our results are highly accurate in practice.

An efficient algorithm for time separation of events in concurrent systems

“…Let the cycle mean of the critical cycle C be T , and the summation of minimum delays values on all edges in the simple cycle C which (i, j) belongs to be P d. Then the maximum slack the edge (i, j) can attain is given by smax(i, j) = T − P i d. Putting the expression for smax(i, j) into Equation 3 gives…”

“…Early research was limited to systems with finite behavior, i.e., those that can be modeled by acyclic graphs [7], [12], [3]. Basic approaches assume a maxcausality operating semantics, while some also handles min-causality, where an event is triggered by the earliest arriving pre-condition.…”

Practical timing analysis of asynchronous circuits using time separation of events

“…Hence, efficient convex optimization techniques cannot be applied to find bounds on the time separations between events. The algorithm of [2], therefore, computes a small convex "envelope" that completely contains the original feasible space. Then, it efficiently computes bounds on the time separation of events in this approximate convex space.…”

“…We compute bounds on the time separations between events using the algorithm of [2]. The basic idea of this algorithm is as follows.…”

“…This allows us to use an efficient time separation of events algorithm [2] to solve both the performance analysis and timing verification problems simultane-…”