Faster Approximation Schemes for Fractional Multicommodity Flow Problems
Περίληψη
Τύπος
Είδος δημοσίευσης σε συνέδριο
Είδος περιοδικού
peer reviewed
Είδος εκπαιδευτικού υλικού
Όνομα συνεδρίου
Όνομα περιοδικού
Acm Transactions on Algorithms
Όνομα βιβλίου
Σειρά βιβλίου
Έκδοση βιβλίου
Συμπληρωματικός/δευτερεύων τίτλος
Περιγραφή
We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of the minimum possible dependencies on the number of commodities k. We show that by modifying the algorithms by Garg and Konemann [1998] and Fleischer [2000], we can reduce their running time on a graph with n vertices and m edges from (O) over tilde(epsilon(-2)(m(2)+ km)) to (O) over tilde(epsilon(-2)m(2)) for an implicit representation of the output, or (O) over tilde(epsilon(-2)(m(2)+ kn)) for an explicit representation, where (O) over tilde (f) denotes a quantity that is O(f log(O(1)) m). The implicit representation consists of a set of trees rooted at sources (there can be more than one tree per source), and with sinks as their leaves, together with flow values for the flow directed from the source to the sinks in a particular tree. Given this implicit representation, the approximate value of the concurrent flow is known, but if we want the explicit flow per commodity per edge, we would have to combine all these trees together, and the cost of doing so may be prohibitive. In case we want to calculate explicitly the solution flow, we modify our schemes so that they run in time polylogarithmic in nk (n is the number of nodes in the network). This is within a polylogarithmic factor of the trivial lower bound of time Omega(nk) needed to explicitly write down a multicommodity flow of k commodities in a network of n nodes. Therefore our schemes are within a polylogarithmic factor of the minimum possible dependencies of the running time on the number of commodities k.
Περιγραφή
Λέξεις-κλειδιά
multicommodity flows, fully-polynomial time approximation schemes, algorithms, packing
Θεματική κατηγορία
Παραπομπή
Σύνδεσμος
<Go to ISI>://000265816600013
http://delivery.acm.org/10.1145/1330000/1328924/a13-karakostas.pdf?ip=195.251.197.109&id=1328924&acc=ACTIVE%20SERVICE&key=C2716FEBFA981EF1E9B06A0954DB6E6FB2E80188D446F61C&CFID=286340637&CFTOKEN=12197681&__acm__=1390819474_04620ef789805273b15953c3a347dfbb
http://delivery.acm.org/10.1145/1330000/1328924/a13-karakostas.pdf?ip=195.251.197.109&id=1328924&acc=ACTIVE%20SERVICE&key=C2716FEBFA981EF1E9B06A0954DB6E6FB2E80188D446F61C&CFID=286340637&CFTOKEN=12197681&__acm__=1390819474_04620ef789805273b15953c3a347dfbb
Γλώσσα
en
Εκδίδον τμήμα/τομέας
Όνομα επιβλέποντος
Εξεταστική επιτροπή
Γενική Περιγραφή / Σχόλια
Ίδρυμα και Σχολή/Τμήμα του υποβάλλοντος
Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών