In an instance of the (directed) Max Leaf Tree (MLT) problem we are given a vertexweighted (di)graph G(V,E,w) and the goal is to compute a subtree with maximum weight on the leaves. The weighted Connected Max Cut (CMC) problem takes in an undirected edgeweighted graph G(V,E,w) and seeks a subset S ⊆ V such that the induced graph G[S] is connected and ∑ e∈δ(S)w(e) is maximized. We obtain a const...

We give a deterministic polynomial-time algorithm which for any given average degree d and asymptotically almost all random graphs G in G(n,m = d2n ) outputs a cut of G whose ratio (in cardinality) with the maximum cut is at least 0.952. We remind the reader that it is known that unless P=NP, for no constant > 0 is there a Max-Cut approximation algorithm that for all inputs achieves an approxim...

We study the boundary of tractability for the Max-Cut problem in graphs. Our main result shows that Max-Cut above the EdwardsErdős bound is fixed-parameter tractable: we give an algorithm that for any connected graph with n vertices and m edges finds a cut of size

We have seen several randomized approximation algorithms before. Recall that for the MAXCUT and MAX-3SAT problems we proved that choosing any solution uniformly at random gives a constant factor approximation in the expectation. For MAX-CUT the approximation factor was 2. For MAX-3SAT, a random assignment of truth values to a variable satisfies a given clause with probability 78 . In the case o...

In this paper we give a flow model on directed multigraphs by introducing reflexions of generalized polymatroids at vertices as constraints for the flow conservation. This model has the essential features of the classical flow model, primarily the max-flow min-cut theorem and the polynomial algorithm for computing the maximal feasible (integral) flow.

What are the economic effects of an interest rate cut when an economy is in the midst of a financial crisis? Under what conditions will a cut stimulate output and employment, and raise welfare? Under what conditions will a cut have the opposite effects? We answer these questions in a general class of open economy models, where a financial crisis is modelled as a time when collateral constraints...

The MAX-CUT problem consists in partitioning the vertex set of a weighted graph into two subsets. The objective is to maximize the sum of weights of those edges that have their endpoints in two different parts of the partition. MAX-CUT is a well known NP-hard problem and it remains NP-hard even if restricted to the class of graphs with bounded maximum degree ∆ (for ∆ ≥ 3). In this paper we stud...