In recent years many algorithms have been proposed in the literature for solving the Max-Cut problem. In this paper we report on the application of a new Tabu Search algorithm to large scale Max-cut test problems. Our method provides best known solutions for many well-known test problems of size up to 10,000 variables, although it is designed for the general unconstrained quadratic binary progr...

In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online max-cut problem, the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which represent permutations over n teams. Another important example is online collaborative filtering...

We study exact algorithms for the max-cut problem. Introducing a new technique, we present an algorithmic scheme that computes a maximum cut in graphs with bounded maximum degree. Our algorithm runs in time O∗(2(1−(2/∆))n). We also describe a max-cut algorithm for general graphs. Its time complexity is O∗(2mn/(m+n)). Both algorithms use polynomial space. Acknowledgements: The work was done whil...

We study max-cut in classes of graphs defined by forbidding a single graph as a subgraph, induced subgraph, or minor. For the first two containment relations, we prove dichotomy theorems. For the minor order, we show how to solve max-cut in polynomial time for the class obtained by forbidding a graph with crossing number at most one (this generalizes a known result for K5-minor-free graphs) and...

Seymour proved that the set of odd circuits of a signed binary matroid (M; ) has the Max-Flow Min-Cut property if and only if it does not contain a minor isomorphic to (M(K4); E(K4)). We give a shorter proof of this result.

We give an algorithm that, with high probability, recovers a planted k-partition in a random graph, where edges within vertex classes occur with probability p and edges between vertex classes occur with probability r ≥ p + c √ p log n/n. The algorithm can handle vertex classes of different sizes and, for fixed k, runs in linear time. We also give variants of the algorithm for partitioning matri...

We present a polynomial time algorithm to find the maximum weight of an edge-cut in graphs embeddable on an arbitrary orientable surface, with integral weights bounded in the absolute value by a polynomial of the size of the graph. The algorithm has been implemented for toroidal grids using modular arithmetics and the generalized nested dissection method. The applications in statistical physics...

An approximation algorithm for Max Cut is designed and analyzed; its performances are experimentally compared with those of a neural algorithm and of the Goemans and Williamson's algorithm.

We give a polynomial time algorithm that given a graph which admits a bisection cutting a fraction (1 − ε) of edges, finds a bisection cutting a (1 − g(ε)) fraction of edges where g(ε) → 0 as ε→ 0. One can take g(ε) = O( 3 √ ε log(1/ε)). Previously known algorithms for Max Bisection could only guarantee finding a bisection that cuts a fraction of edges bounded away from 1 (in fact less than 3/4...

We give the rst polynomial time approximability characterization of dense weighted instances of MAX-CUT, and some other dense weighted NP-hard problems in terms of their empirical weight distributions. This gives also the rst almost sharp characterization of inapproximability of unweighted 0,1 MAX-BISECTION instances in terms of their density parameter only.