A new polynomial-time algorithm for linear programming
Combinatorica
An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Testing for cycles in infinite graphs with periodic structure
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Strongly polynomial-time and NC algorithms for detecting cycles in dynamic graphs
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Study of parallelism in regular iterative algorithms
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Recognizing strong connectivity in (dynamic) periodic graphs and its relation to integer programming
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Analysis of free schedule in periodic graphs
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs
Journal of the ACM (JACM)
Achieving Full Parallelism Using Multidimensional Retiming
IEEE Transactions on Parallel and Distributed Systems
Polynomial algorithms for minimum cost paths in periodic graphs
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
FunState—an internal design representation for codesign
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
Discrete Event Dynamic Systems
Fully Parallel Hardware/Software Codesign for Multi-Dimensional DSP Applications
CODES '96 Proceedings of the 4th International Workshop on Hardware/Software Co-Design
Church synthesis problem for noisy input
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Energy games in multiweighted automata
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
The complexity of mean-payoff automaton expression
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Hyperplane separation technique for multidimensional mean-payoff games
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
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Consider a digraph which has labels on its edges which are k-dimensional vectors. In this paper we show it is possible in polynomial time to determine if such a digraph contains a zero cycle, i.e., a cycle whose edge labels sum to the zero vector component-wise. This solves the open problem of finding cycles in dynamic graphs which was posed by Iwano and Steiglitz. Our solution has a time complexity of &Ogr;(|V| log(|V|)Z) where Z is the complexity of a linear programming problem. For the important cases of two and three dimensions we present &Ogr;(Z) time algorithms. The linear programming problems we solve have at most 2|E| variables and &Ogr;(|E| + |V| + k) constraints.