Experimental Evaluation of Parametric Max-Flow Algorithms

  title={Experimental Evaluation of Parametric Max-Flow Algorithms},
  author={Maxim A. Babenko and Jonathan Derryberry and Andrew V. Goldberg and Robert Endre Tarjan and Yunhong Zhou},
  booktitle={Workshop on Engineering Applications},
The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric… 

Structural and algorithmic properties for parametric minimum cuts

This work defines two conditions on parametrized arc capacities that are necessary and sufficient for (strictly) decreasing differences of the parametric cut function and shows how to construct appropriate Flow Updates in linear time under these conditions.

Monotonicity and conformality in multicommodity network‐flow problems

The objective of this paper is to develop a monotonicity theory for the important class of minimum convex‐cost parametric multicommodity network‐flow problems defined over directed graphs. The

Flows in almost linear time via adaptive preconditioning

This work gives an alternate approach for approximating undirected max-flow, and the first almost-linear time approximations of discretizations of total variation minimization objectives.

Potts Model, Parametric Maxflow and K-Submodular Functions

The technique to reduce the runtime to O(log k) maxflow computations (or one parametric maxflow computation) is shown, which allows to speed-up the subsequent alpha expansion for the unlabeled part, or can be used as it is for time-critical applications.

Oracle-guided search in sorted matrices improving balanced flow compuatation

In a successor search we are given a key x and a set A from a totally ordered universe and search for the smallest element of A that is larger than or equal to x. It is well known that the number of

Parametric Maxflows for Structured Sparse Learning with Convex Relaxations of Submodular Functions

It is shown that the parametric maxflow algorithm proposed by Gallo et al. and its variants, which runs, in the worst-case, at the cost of only a constant factor of a single computation of the corresponding maxflow optimization, can be adapted to solve the proximal problems for those penalties.

Two-Level Push-Relabel Algorithm for the Maximum Flow Problem

A two-level push-relabel algorithm for the maximum flow problem and compare it to the competing codes to generalize a practical algorithm for bipartite flows.

Learning with Submodular Functions: A Convex Optimization Perspective

  • F. Bach
  • Computer Science
    Found. Trends Mach. Learn.
  • 2013
In Learning with Submodular Functions: A Convex Optimization Perspective, the theory of submodular functions is presented in a self-contained way from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems.

Finding dense and isolated submarkets in a sponsored search spending graph

This work introduces an efficient algorithm for finding submarkets that are optimal for a user-specified tradeoff between these three quantities in a large spending graph from Yahoo! sponsored search.

Title On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows Permalink

This paper recalls in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. and Luckhaus and Sturzenhecker, and shows how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques.



Balancing Applied to Maximum Network Flow Problems

It is shown that a standard monotonic parametric maximum flow problem can be formulated as a problem of computing a particular maximum flow that is balanced in an appropriate sense, and a divide-and-conquer algorithm is presented to compute such a balanced flow in a logarithmic number of ordinary maximum-flow computations.

A Fast Parametric Maximum Flow Algorithm and Applications

It is shown that the recent maximum flow algorithm of Goldberg and Tarjan can be extended to solve an important class of such parametric maximum flow problems, at the cost of only a constant factor in its worst-case time bound.

A new approach to the maximum flow problem

By incorporating the dynamic tree data structure of Sleator and Tarjan, a version of the algorithm running in O(nm log(n'/m)) time on an n-vertex, m-edge graph is obtained, as fast as any known method for any graph density and faster on graphs of moderate density.

The Pseudoflow Algorithm and the Pseudoflow-Based Simplex for the Maximum Flow Problem

This is the first known simplex algorithm for maximum flow that generates all possible breakpoints of parameter values in the same complexity as required to solve a single maximum flow instance and the fastest one.

Beyond the flow decomposition barrier

  • A. GoldbergSatish Rao
  • Mathematics
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
Borders are improved for the Gomory-Hu tree problem, the parametric flow problem, and the approximate s-t cut problem by introducing a new approach to the maximum flow problem.

Simultaneous Parametric Maximum Flow Algorithm with Vertex Balancing

SPMF replaces the path-wise flow augmentation by flow-redistribution at each node, which provides a factor of ten speed-up for all the large datasets tested, and the new algorithms are monotone convergent.

On Implementing the Push—Relabel Method for the Maximum Flow Problem

Efficient implementations of the push—relabel method for the maximum flow problem are studied, showing that the highest-level selection strategy gives better results when combined with both global and gap relabeling heuristics.

Algorithms - ESA 2006, 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006, Proceedings

Invited Lectures.- Origami, Linkages, and Polyhedra: Folding with Algorithms.- Reliable and Efficient Geometric Computing.- Some Computational Challenges in Today's Bio-medicine.- Contributed Papers:

On Implementing Push-Relabel Method for the Maximum Flow Problem

The resulting codes are faster than the previous codes, and much faster on some problem families, due to the combination of heuristics used in the implementation of the push-relabel method.

Improved Algorithms for Bipartite Network Flow

It is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks, and ideas are extended to dynamic tree implementations, parametric maximum flows, and minimum-cost flows.