Shortest path and maximum flow problems in networks with additive losses and gains

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 d...

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Bibliographic Details
Published inTheoretical computer science Vol. 412; no. 4; pp. 391 - 401
Main Authors Brandenburg, Franz J., Cai, Mao-cheng
Format Journal Article
LanguageEnglish
Published Oxford Elsevier B.V 04.02.2011
Elsevier
Subjects
[formula omitted]-hard problems
Additives
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation
C (programming language)
Computer science; control theory; systems
Exact sciences and technology
Extended networks
Gain
Lossy and gainy arcs
Max-flow problems
Miscellaneous
Networks
Shortest path problems
Theoretical computing
Transportation
Unit-loss networks
Unit-loss networks
Lossy and gainy arcs
Shortest path problems
Max-flow problems
Extended networks
NP -hard problems
Data analysis
Costs
Network flow
Computer theory
Shortest path
Unit
N P-hard problems
Polynomial time
Maximum
Financial data
Data communication
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2010.11.019