On flows in simple bidirected and skew-symmetric networks

On flows in simple bidirected and skew-symmetric networks We consider a simple directed network. Results of Karzanov, Even, and Tarjan show that the blocking flow method constructs a maximum integer flow in this network in O(m min (m 1/2, n 2/3)) time (hereinafter, n denotes the number of nodes, and m the number of arcs or edges). For the bidirected case, Gabow proposed a reduction to solve the maximum integer flow problem in O(m 3/2) time. We show that, with a variant of the blocking flow method, this problem can also be solved in O(mn 2/3) time. Hence, the gap between the complexities of directed and bidirected cases is eliminated. Our results are described in the equivalent terms of skew-symmetric networks. To obtain the time bound of O(mn 2/3), we prove that the value of an integer s-s′ flow in a skew-symmetric network without parallel arcs does not exceed O(Un 2/d 2), where d is the length of the shortest regular s-s′ path in the split network and U is the maximum arc capacity. We also show that any acyclic integer flow of value v in a skew-symmetric network without parallel arcs can be positive on at most O(n√v) arcs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On flows in simple bidirected and skew-symmetric networks

Loading next page...
Copyright © 2006 by Pleiades Publishing, Inc.
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial