In this paper, we investigate the Max-Cut problem and propose a probabilistic heuristic to address its classic and weighted version. Our approach is based on the Estimation of Distribution Algorithm (EDA) that creates a population of individuals capable of evolving at each generation towards the global solution. We have applied the MaxCut problem for image segmentation and defined the edges’ we...

The field of cryo-electron microscopy has made astounding advancements in the past few years, mainly due to improvements in the hardware of the microscopes. Yet, one of the key open challenges of the field remains the processing of heterogeneous data sets, produced from samples containing particles at several different conformational states. For such data sets, one must first classify their ima...

Two simple approximation algorithms for the minimum k-cut problem are presented. Each algorithm finds a k cut having weight within a factor of (2 2/k) of the optimal. One algorithm is particularly efficient-it requires a total of only n maximum flow computations for finding a set of near-optimal k cuts, one for each value of k between 2 and n.

Given a bipartite graph G = (V1, V2, E) where edges take on both positive and negative weights from set S , the maximum weighted edge biclique problem, or S-MWEB for short, asks to find a bipartite subgraph whose sum of edge weights is maximized. This problem has various applications in bioinformatics, machine learning and databases and its (in)approximability remains open. In this paper, we sh...

Erdős posed the problem of finding conditions on a graph G that imply t (G)= b(G), where t (G) is the largest number of edges in a triangle-free subgraph and b(G) is the largest number of edges in a bipartite subgraph. Let δc be the least number so that any graph G on n vertices with minimum degree δcn has t (G)= b(G). Extending results of Bondy, Shen, Thomassé and Thomassen we show that 0.75 δ...

A co-bipartite chain graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cut problem (MaxCut) is NP-hard in co-bipartite graphs [3]. We consider MaxCut in co-bipartite chain graphs. We first consider the twin-free case and present an explicit solution. We then show that MaxCut is ...

In this paper, the potential of the path relinking method for the maximum cut problem is investigated. This method is embedded within global equilibrium search to utilize the set of high quality solutions provided by the latter. The computational experiment on a set of standard benchmark problems is provided to study the proposed approach. The empirical experiments reveal that the large sizes o...

In this paper, we propose a simple and natural randomized algorithm to embed a tree T in a given graph G. The algorithm can be viewed as a “self-avoiding tree-indexed random walk”. The order of the tree T can be as large as a constant fraction of the order of the graph G, and the maximum degree of T can be close to the minimum degree of G. We show that our algorithm works in a variety of intere...

For a positive integer m, let f(m) be the maximum value t such that any graph with m edges has a bipartite subgraph of size at least t, and let g(m) be the minimum value s such that for any graph G with m edges there exists a bipartition V (G) = V1 ∪ V2 such that G has at most s edges with both incident vertices in Vi. Alon proved that the limsup of f(m)− (m/2 + √ m/8) tends to infinity as m te...