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Table 3 Performance of the software packages measured in wall-time (i.e., elapsed time), and CPU seconds (for the computations running on the cluster)

From: A roadmap for the computation of persistent homology

Data set

(a) Computations on cluster: wall-time seconds

eleg

Klein

HIV

drag 2

random

genome

Size of complex

4.4 × 106

1.1 × 107

2.1 × 108

1.3 × 109

3.1 × 109

4.5 × 108

Max. dim.

2

2

2

2

8

2

javaPlex (st)

84

747

-

-

-

-

Dionysus (st)

474

1,830

-

-

-

-

DIPHA (st)

6

90

1,631

142,559

-

9,110

Perseus

543

1,978

-

-

-

-

Dionysus (d)

513

145

-

-

-

-

DIPHA (d)

4

6

81

2,358

5,096

232

Gudhi

36

89

1,798

14,368

-

4,753

Ripser

1

1

2

6

349

3

Data set

(b) Computations on cluster: CPU seconds

eleg

Klein

HIV

drag 2

random

genome

Size of complex

4.4 × 106

1.1 × 107

2.1 × 108

1.3 × 109

3.1 × 109

4.5 × 108

Max. dim.

2

2

2

2

8

2

javaPlex (st)

284

1,031

-

-

-

-

Dionysus (st)

473

1,824

-

-

-

-

DIPHA (st)

68

1,360

25,950

1,489,615

-

130,972

Perseus

542

1,974

-

-

-

-

Dionysus (d)

513

145

-

-

-

-

DIPHA (d)

39

73

1,276

37,572

79,691

3,622

Gudhi

36

88

1,794

14,351

-

4,764

Ripser

1

1

2

5

348

2

Data set

(c) Computations on shared-memory system: wall-time seconds

eleg

Klein

HIV

drag 2

genome

fract r

Size of complex

3.2 × 108

1.1 × 107

2.1 × 108

1.3 × 109

4.5 × 108

2.8 × 109

Max. dim.

3

2

2

2

2

3

javaPlex (st)

13,607

1,358

43,861

-

28,064

-

Perseus

-

1,271

-

-

-

-

Dionysus (d)

-

100

142,055

35,366

-

572,764

DIPHA (d)

926

13

773

4,482

1,775

3,923

Gudhi

381

6

177

1,518

442

4,590

Ripser

2

1

2

5

3

1,517

  1. For each data set, we indicate the size of the simplicial complex and the maximum dimension up to which we construct the VR complex. For all data sets, we construct the filtered VR complex up to the maximum distance between any two points. We indicate the implementation of the standard algorithm using the abbreviation ‘st’ following the name of the package, and we indicate the implementation of the dual algorithm using the abbreviation ‘d.’ The symbol ‘-’ signifies that we were unable to finish computations for this data set, because the machine ran out of memory. Perseus implements only the standard algorithm, and Gudhi and Ripser implement only the dual algorithm. (a), (b) We run DIPHA on one node and 16 cores for the data sets eleg, Klein, and genome; on 2 nodes of 16 cores for the HIV data set; on 2 and 3 nodes of 16 cores for the dual and standard implementations, respectively, for drag 2; and on 8 nodes of 16 cores for random. (The maximum number of processes that we could use at any one time was 128.) (c) We run DIPHA on a single core.
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