zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new proximal decomposition algorithm for routing in telecommunication networks. (English) Zbl 1015.90020
Summary: We present a new and much more efficient implementation of the proximal decomposition algorithm for routing in congested telecommunication networks. The routing model that we analyze is a static one intended for use as a subproblem in a network design context. After describing our new implementation of the proximal decomposition algorithm and reviewing the flow deviation algorithm, we compare the solution times for (1) the original proximal decomposition algorithm, (2) our new implementation of the proximal decomposition algorithm, and (3) the flow deviation algorithm. We report extensive computational comparisons of solution times using actual and randomly generated networks. These results show that our new proximal decomposition algorithm is substantially faster than the earlier proximal decomposition algorithm in every case. Our new proximal decomposition is also faster than the flow deviation algorithm if the network is not too congested and a highly accurate solution is desired, such as one within 0.1% of optimality. For moderate accuracy requirements, such as 1.0% optimality, and for congested networks, the flow deviation algorithm is faster. More importantly, solutions that we obtained from the proximal decomposition algorithm always involve flow on only a small number of routes between source-destination pairs. The flow deviation algorithm, however, can produce solutions with flows on a very large number of different routes between individual source-destination pairs.
90B18Communication networks (optimization)
49M27Decomposition methods in calculus of variations