Divide-and-conquer approximation algorithms via spreading metrics

Author:

Even Guy1,Naor Joseph Seffi2,Rao Satish3,Schieber Baruch4

Affiliation:

1. Tel-Aviv Univ., Tel-Aviv, Israel

2. Technion–Israel Institute of Technology, Haifa, Israel

3. Univ. of California, Berkeley

4. IBM T. J. Watson Research Center, Yorktown Heights, NY

Abstract

We present a novel divide-and-conquer paradigm for approximating NP-hard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divide-and-conquer approach is applicable. Second, a fractional spreading metric is computable in polynomial time. The spreading metric assigns lengths to either edges or vertices of the input graph, such that all subgraphs for which the optimization problem is nontrivial have large diameters. In addition, the spreading metric provides a lower bound, τ, on the cost of solving the optimization problem. We present a polynomial time approximation algorithm for problems modeled by our paradigm whose approximation factor is O (min{log τ, log log τ, log k log log k }) where k denotes the number of “interesting” vertices in the problem instance, and is at most the number of vertices. We present seven problems that can be formulated to fit the paradigm. For all these problems our algorithm improves previous results. The problems are: (1) linear arrangement; (2) embedding a graph in a d -dimensional mesh; (3) interval graph completion; (4) minimizing storage-time product; (5) subset feedback sets in directed graphs and multicuts in circular networks; (6) symmetric multicuts in directed networks; (7) balanced partitions and p -separators (for small values of p ) in directed graphs.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Reference26 articles.

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