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3. Dijkstra’ssingle-sourceshortestpaths(dijkstra), 4. directedclusteringcoefficients(dirclustercoeffs), 5. Prim’sminimumspanningtree(prim_mst),and 6. clusteringcoefficients(clustercoeffs), in two cases: • standardMatlabsparsematrixinput(standard),and • “pre-converted”input(fast). In MatlabBGL and gaimc, the input must be transposed or converted to compressed-sparse row arrays, respectively. In the second case, we show the performance with inputs that are already converted, which corresponds to a faster function call. We evaluate each function on either a small set of sample graphs (dfs and dijkstra) or a set of synthetic graphs (scomponents, dirclustercoeffs, prim_mst, and clustercoeffs). For each function, we call it once to ensure that the Matlab just-in-time compiler has the current version compiled. The two search functions that begin with a source vertex—dfs and dijkstra— are called on each of the graphs listed in table 6.2 with 100 random starting vertices, and every test is repeated 30 times. The functions scomponents and dirclustercoeffs are evaluated on 30 instances of random directed graphs with 25 edges per row and 10, 100, 5000, 10000, and 50000 vertices. The function clustercoeffs is evaluated similarly, but with random symmetric graphs instead. Finally, the minimum spanning tree function is evaluated on 30 instances of a random symmetric graph with average degree 25 and 100, 5000, and 10000 vertices. The aggregated results of all these tests are shown in figure 6.4. Graph allsp1 clr24-1 wb-cs.stan minnesota tapir Verts. 5 9 9914 2642 1024 Edges 9 14 36584 3303 2846 6.4 ⋅ gaimc 151 Table 6.2 – gaimc evaluation graphs. 14 12 10 8 6 4 2 0 Standard Fast dfs scomponents dijkstra dirclustercoeffs mst_prim clustercoeffs Figure6.4–Performanceofthegaimclibrary. Anexperimentalcomparisonoftheperformance of the gaimc library to MatlabBGL shows that many functions in gaimc take only twice as much time as their MatlabBGL counterparts. The difference between the standard and fast operations is that fast operations eliminate any data translations and measure pure algorithm speed. Standard calls in these libraries involve some data translation, which is included in the time for the standard operations. SlowdownPDF Image | Instagram Cheat Sheet
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