  The state-of-the-art modern pose-graph optimization (PGO) systems are vertex
based. In this context the number of variables might be high, albeit the number
of cycles in the graph (loop closures) is relatively low. For sparse problems
particularly, the cycle space has a significantly smaller dimension than the
number of vertices. By exploiting this observation, in this paper we propose an
alternative solution to PGO, that directly exploits the cycle space. We
characterize the topology of the graph as a cycle matrix, and re-parameterize
the problem using relative poses, which are further constrained by a cycle
basis of the graph. We show that by using a minimum cycle basis, the
cycle-based approach has superior convergence properties against its
vertex-based counterpart, in terms of convergence speed and convergence to the
global minimum. For sparse graphs, our cycle-based approach is also more time
efficient than the vertex-based. As an additional contribution of this work we
present an effective algorithm to compute the minimum cycle basis. Albeit known
in computer science, we believe that this algorithm is not familiar to the
robotics community. All the claims are validated by experiments on both
standard benchmarks and simulated datasets. To foster the reproduction of the
results, we provide a complete open-source C++ implementation (Code:
\url{https://bitbucket.org/FangBai/cycleBasedPGO) of our approach.
