A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs
Journal of the ACM (JACM)
Algorithms for finding a fundamental set of cycles for an undirected linear graph
Communications of the ACM
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
A shortest path approach to wireframe to solid model conversion
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
A new viewpoint on code generation for directed acyclic graphs
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A preprocessor for the via minimization problem
DAC '86 Proceedings of the 23rd ACM/IEEE Design Automation Conference
ACM Transactions on Mathematical Software (TOMS)
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
Communications of the ACM
An algorithm for the blocks and cutnodes of a graph
Communications of the ACM
An efficient search algorithm to find the elementary circuits of a graph
Communications of the ACM
Circuit enumeration in an undirected graph
ACM-SE 16 Proceedings of the 16th annual Southeast regional conference
Minimum Cycle Bases and Their Applications
Algorithmics of Large and Complex Networks
Benchmarks for strictly fundamental cycle bases
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
An application of rough sets to graph theory
Information Sciences: an International Journal
Hi-index | 48.27 |
A fast method is presented for finding a fundamental set of cycles for an undirected finite graph. A spanning tree is grown and the vertices examined in turn, unexamined vertices being stored in a pushdown list to await examination. One stage in the process is to take the top element v of the pushdown list and examine it, i.e. inspect all those edges (v, z) of the graph for which z has not yet been examined. If z is already in the tree, a fundamental cycle is added; if not, the edge (v, z) is placed in the tree. There is exactly one such stage for each of the n vertices of the graph. For large n, the store required increases as n2 and the time as n&ggr; where &ggr; depends on the type of graph involved. &ggr; is bounded below by 2 and above by 3, and it is shown that both bounds are attained.In terms of storage our algorithm is similar to that of Gotlieb and Corneil and superior to that of Welch; in terms of speed it is similar to that of Welch and superior to that of Gotlieb and Corneil. Tests show our algorithm to be remarkably efficient (&ggr; = 2) on random graphs.