In this post, I will summarize the results obtained with the inclusion in Sage of Boost and igraph libraries. This was the main part of my Google Summer of Code project, and it was completed yesterday, when ticket 19003 was closed.

We have increased the number of graph algorithms available in Sage from 66 to 98 (according to the list used in the initial comparison of the graph libraries [1]). Furthermore, we decreased the running-time of several Sage algorithms: in some cases, we have been able to improve the asymptotic running-time, obtaining up to 10000x improvements in our tests. Finally, during the inclusion of external algorithms, we have refactored and cleaned some of Sage source code, like the shortest path routines: we have standardized the input and the output of 15 routines related to shortest paths, and we have removed duplicate code as much as possible.

More specifically, the first part of the project was the inclusion of Boost graph library: since the library is only available in C++, we had to develop an interface. This interface lets us convert easily a Sage graph into a Boost graph, and run algorithms on the converted graph. Then, we have written routines to re-translate the output into a Sage-readable format: this way, the complicated Boost library is "hidden", and users can interact with it as they do with Sage. In particular, we have interfaced the following algorithms:

- Edge connectivity (trac.sagemath.org/ticket/18564);
- Clustering coefficient (trac.sagemath.org/ticket/18811);
- Cuthill-McKee and King vertex orderings (trac.sagemath.org/ticket/18876);
- Minimum spanning tree (trac.sagemath.org/ticket/18910);
- Dijkstra, Bellman-Ford, Johnson shortest paths (trac.sagemath.org/ticket/18931);

In the second part of the project, we included igraph: since this library already offers a Python interface, we decided to include it as an optional package (before it becomes a standard package, at least an year should pass [2]). To install the package, it is enough to type the following instruction from the Sage root folder:

sage -i igraph # To install the igraph C core

sage -i python_igraph # To install the Python interface

Then, we can easily interact with igraph: for a list of available routines, it is enough to type "igraph." and click tab twice. To convert a Sage graph g_sage into an igraph graph it is enough to type g_igraph = g_sage.igraph_graph(), while a Sage graph can be instantiated from an igraph graph through g_sage=Graph(g_igraph) or g_sage=DiGraph(g_igraph). This way, all igraph algorithms are now available in Sage.

Furthermore, we have included the igraph maximum flow algoritm inside the Sage corresponding function, obtaining significant improvements (for more information and benchmarks, we refer to ticket 19003 [3]).

In conclusion, I think the project reached its main goal, the original plan was followed very closely, and we have been able to overcome all problems.

Before closing this post, I would like to thank many people that helped me with great advices, and who provided great solutions to all the problems I faced. First of all, my mentor David Coudert: he always answered very fast to all my queries, and he gave me great suggestions to improve the quality of the code I wrote. Then, a very big help came from Nathann Cohen, who often cooperated with David in reviewing my code and proposing new solutions. Moreover, I have to thank Martin Cross, who gave me good suggestions with Boost graph library, and Volker Braun, who closed all my ticket. Finally, I have to thank the whole Sage community for giving me this great opportunity!

[1] https://docs.google.com/spreadsheets/d/1Iu1hkQtRn9J-sgfZbQTu2RoXzyjoMEWP5-cm3nAwnWE/edit?usp=sharing

[2] http://doc.sagemath.org/html/en/developer/coding_in_other.html

[3] http://trac.sagemath.org/ticket/19003