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1. Random Sampling Database of PerfectClub

In 6_fig:PerfectClub_satisfiability_dimension_JV64_LS64_100, the histogram legends show three colors red, blue and green. The meanings of these legends are: the red zones present the cases where JANUS 64-bit is faster than $C^3$ Simplex 64-bit; the green zones correspond to the cases where $C^3$ Simplex 64-bit is faster than JANUS 64-bit; the blue zones mean that our implementation cannot tell which one is faster than the other, i.e. the run times cannot be compared because of the time resolution used.

This histogram has two axes representing the numbers of variables in the constraint systems, also known as the space dimensions of the corresponding polyhedra, and the number of constraint systems available in PerfectClub polyhedral sampled database, for the satisfiability test operator. We can see this information in the first line of the figure header, as well the percentages: JANUS 64-bit is faster for $25$ percent of all tests, $C^3$ Simplex 64-bit is never faster. It also means that in $75$ percent of cases we cannot compare the execution times, due to the time resolution.

Furthermore, total accumulated run times for all tests are compared, from which the global acceleration is derived and displayed in the second line of figure header: the total run time of $C^3$ Simplex 64-bit is divided by the total run time of JANUS 64-bit which shows that JANUS 64-bit is approximately $22$ times faster than $C^3$ Simplex 64-bit on average.

Figure 13: PerfectClub: Dimension JANUS 64-bit vs $C^3$ Simplex 64-bit in sampled database
\begin{figure}
\centering\epsfig {file=POLYBENCH_evaluations/PerfectClub_JV64_LS...
..._DATABASE_100/dimension_JV64_LS64_crite.eps,height=5.9cm,width=14cm}\end{figure}

The same information is represented in 6_fig:PerfectClub_satisfiability_nb_eq_JV64_LS64_100 and 6_fig:PerfectClub_satisfiability_nb_ineq_JV64_LS64_100, with respect to the number of equations and number of inequalities respectively.

Figure 14: PerfectClub: Numbers of equations JANUS 64-bit vs $C^3$ Simplex 64-bit in sampled database
\begin{figure}
\centering\epsfig {file=POLYBENCH_evaluations/PerfectClub_JV64_LS...
...2005_DATABASE_100/nb_eq_JV64_LS64_crite.eps,height=5.9cm,width=14cm}\end{figure}

Figure 15: PerfectClub: Numbers of inequalities JANUS 64-bit vs $C^3$ Simplex 64-bit in sampled database
\begin{figure}
\centering\epsfig {file=POLYBENCH_evaluations/PerfectClub_JV64_LS...
...05_DATABASE_100/nb_ineq_JV64_LS64_crite.eps,height=5.9cm,width=14cm}\end{figure}

We can see that the histogram with dimension axis is more informative than the other two. This remark holds for all the results, hence from now on we only present histograms with respect to the dimension.


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Previous: 1. JANUS 64-bit versus Up: 1. JANUS 64-bit versus Next: 2. Biased Database of
Nguyen Que Duong
2006-09-16