The problem of efficiently shaping downlink data bursts into rectangles and packing them in the OFDMA subframe is not addressed by the IEEE 802.16 standard, and is left as an implementation issue. In this paper, we propose a linear complexity bursts packing algorithm to maximize radio resources usage on the OFDMA downlink. Our scheme shapes the bursts into identical width, places them in column direction and maximally fills the columns by shifting the bursts on different columns. By simulation, we show that the scheme can push the radio resource usage over 95%, which is on average 20% improvement compared with the simple 2D fixed-bin strip packing and 8% improvement with the exhaustive search. Moreover, the proposed scheme is also power-efficient, because subscriber stations (SSs) do not need to receive a large aggregated burst created for packing problem complexity reduction.

Circuits can be simplified for combinational equivalence checking by transforming internal functions, while preserving their ranges. In this paper, we investigate how to effectively apply the idea to improve equivalence checking. We propose new heuristics to identify groups of nets in a cut, and elaborate detailed aspects of the new equivalence checking method. With a given miter, we identify a group of nets in a cut and transform the function of each net into a more compact representation with less variables. These new compact parametric representations preserve the range of nets as well as of the cut. This transformation significantly reduces the size of intermediate BDDs and enables the verification to be conclusive for many designs which state-of-the-art equivalence checkers fail to verify. Iterative groupings and transformations are performed until no grouping is possible for a cut. Then we proceed to the next cut and continue until the compare point is reached. Our experimental results show the effectiveness of our strategy and new grouping heuristics on the new method.

We propose a unifying method for analysis of scheduling problems in real-time systems. The method is based on ACSR-VP, a real-time process algebra with value-passing capabilities. We use ACSR-VP to describe an instance of a scheduling problem as a process that has parameters of the problem as free variables. The specification is analyzed by means of a symbolic algorithm. The outcome of the analysis is a set of equations, a solution to which yields the values of the parameters that make the system schedulable. Equations are solved using integer programming or constraint logic programming. The paper presents specifications of two scheduling problems as examples.