Fig. 1. Processor i requests work from i4 when its best-node rank relative to {i,i4} deteriorates beyond the threshold value s.

Fig. 2. To regulate overhead due to load-information exchange, instead of processors reporting c_τ whenever it changes, they now report c_τ2 whenever either the current c_τ1 exceeds the c_τ2 at the time of the last load-information report, or the current c_τ2 is smaller than the c_τ2 previously reported, a less likely event. Qualitative load-information exchange frequency and overhead is then inversely related to threshold cost interval δ=τ₂−τ₁+1.

Fig. 3. Flow chart of the adaptive QE strategy illustrating its main components. Steps indicated above are executed by all processors in parallel.

Table 1.

Comparison of speedups obtained by the adaptive and non-adaptive QE strategies for five problems from the MIPLIB benchmark suite on 16 processors of an IBM SP2.

Columns 1–11 of the table provide the following information: (1) problem name, (2) number of constraints, (3) number of variables, (4) number of integer variables, (5) number of integer variables that are binary, (6) number of essential nodes, (7) execution time on 16 processors, (8) interconnect type, (9) speedup obtained with adaptive QE, (10) speedup improvement obtained with adaptive QE over non-adaptive QE speedup

Table 2. Speedups obtained using adaptive QE strategy for two problems from the MIPLIB benchmark suite, one with the maximum number of non-binary integer variables (bell3a) and the other with the maximum number of constraints (rentacar)