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
Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem
Mathematics of Operations Research
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
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Cycles in Generalized Networks
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow
Mathematics of Operations Research
| Hi-index | 5.23 |
We introduce networks with additive losses and gains on the arcs. If a positive flow of x units enters an arc a, then x+g(a) units exit. Arcs may increase or consume flow, i.e., they are gainy or lossy. Such networks have various applications, e.g., in financial analysis, transportation, and data communication. Problems in such networks are generally intractable. In particular, the shortest path problem is NP-hard. However, there is a pseudo-polynomial time algorithm for the problem with nonnegative costs and gains. The maximum flow problem is strongly NP-hard, even in networks with integral capacities and with unit gain or with loss two on the arcs, and is hard to approximate. However, it is solvable in polynomial time in unit-loss networks using the Edmonds-Karp algorithm. Our NP-hardness results contrast efficient polynomial time solutions of path and flow problems in standard and in so-called generalized networks with multiplicative losses and gains.