A polynomial-time algorithm to find the shortest cycle basis of a graph
SIAM Journal on Computing
A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
On finding a cycle basis with a shortest maximal cycle
Information Processing Letters
Periodic network optimization with different arc frequencies
Discrete Applied Mathematics
Algorithms for Generating Fundamental Cycles in a Graph
ACM Transactions on Mathematical Software (TOMS)
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Planar 3-colorability is polynomial complete
ACM SIGACT News
Minimum Cycle Bases for Network Graphs
Algorithmica
Discrete Applied Mathematics
SIAM Journal on Computing
The First Optimized Railway Timetable in Practice
Transportation Science
Minimum cycle bases: Faster and simpler
ACM Transactions on Algorithms (TALG)
A greedy approach to compute a minimum cycle basis of a directed graph
Information Processing Letters
Benchmarks for strictly fundamental cycle bases
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
The modeling power of the periodic event scheduling problem: railway timetables-and beyond
ATMOS'04 Proceedings of the 4th international Dagstuhl, ATMOS conference on Algorithmic approaches for transportation modeling, optimization, and systems
A cut-based heuristic to produce almost feasible periodic railway timetables
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Computing delay resistant railway timetables
Computers and Operations Research
Cyclic matrices of weighted digraphs
Discrete Applied Mathematics
Exact formulations and algorithm for the train timetabling problem with dynamic demand
Computers and Operations Research
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Cyclic railway timetables are typically modeled by a constraint graph G with a cycle period time T, in which a periodic tension x in G corresponds to a cyclic timetable. In this model, the periodic character of the tension x is guaranteed by requiring periodicity for each cycle in a strictly fundamental cycle basis, that is, the set of cycles generated by the chords of a spanning tree of G. We introduce the more general concept of integral cycle bases for characterizing periodic tensions. We characterize integral cycle bases using the determinant of a cycle basis, and investigate further properties of integral cycle bases. The periodicity of a single cycle is modeled by a so-called cycle integer variable. We exploit the wider class of integral cycle bases to find tighter bounds for these cycle integer variables, and provide various examples with tighter bounds. For cyclic railway timetabling in particular, we consider Minimum Cycle Bases for constructing integral cycle bases with tight bounds.