A new polynomial-time algorithm for linear programming
Combinatorica
Data structures and network algorithms
Data structures and network algorithms
Introduction to algorithms
Combinatorial algorithms for the generalized circulation problem
Mathematics of Operations Research
A strongly polynomial algorithm for a special class of linear programs
Operations Research
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Improved Algorithms for Linear Inequalities with Two Variables per Inequality
SIAM Journal on Computing
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Computer networks (3rd ed.)
Combinatorial approximation algorithms for generalized flow problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster approximation algorithms for generalized flow
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Combinatorial approximation algorithms for generalized flow problems
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Journal of Algorithms
Shortest Path and Maximum Flow Problems in Networks with Additive Losses and Gains
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Shortest path and maximum flow problems in networks with additive losses and gains
Theoretical Computer Science
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Generalized networks specify two parameters for each arc, a cost and a gain. If x units enter an arc a, then x 驴 g(a) exit. Arcs may generate or consume flow, i.e., they are gainy or lossy. The objective is a cheapest path of a unit flow from the source (SGSP) and the single-pair cheapest path (SPGSP).There are several types of negative cycles. A lossy cycles decreases the gain. Then even a negative cost cycle has only bounded cost. A gainy cycle increases the flow. Then even a positive cost cycle may induce a total cost of minus infinity.We solve SGSP by an extension of the Bellman-Ford algorithm. At the heart of the algorithm is a new and effective cycle detection strategy. The algorithm solves SGSP in O(nm log n), which improves to O(nm) in lossless networks and to O(n log n + m) in a monotone setting. Our algorithm is simpler and at least a factor of O(n) faster than the previous algorithms using linear programming or complex parametric search and scaling techniques. This improvement is a big step for such a well-investigated problem.To the contrary, the single-pair generalized shortest path problem SPGSP is NP-hard, even with nonnegative costs and uniformly lossy arcs.