A tabu search heuristic based on k-diamonds for the weighted feedback vertex set problem

Given an undirected and vertex weighted graph G = (V,E,w), the Weighted Feedback Vertex Problem (WFVP) consists of finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard and to be polynomially solvable on some special classes of graphs (e.g., interval graphs, co-comparability graphs, diamond graphs). In this paper we introduce an extension of diamond graphs, namely the k-diamond graphs, and give a dynamic programming algorithm to solve WFVP in linear time on this class of graphs. Other than solving an open question, this algorithm allows an efficient exploration of a neighborhood structure that can be defined by using such a class of graphs. We used this neighborhood structure inside our Iterated Tabu Search heuristic. Our extensive experimental show the effectiveness of this heuristic in improving the solution provided by a 2-approximate algorithm for the WFVPon general graphs

an evolutionary approach for the offsetting inventory cycle problem

AbstractIn inventory management, a fundamental issue is the rational use of required space. Among the numerous techniques adopted, an important role is played by the determination of the replenishment cycle offsetting which minimizes the warehouse space within a considered time horizon. The NP-completeness of the Offsetting Inventory Cycle Problem (OICP) has led the researchers towards the development and the comparison of specific heuristics. We propose and implement a genetic algorithm for the OICP, whose effectiveness is validated by comparing its solutions with those found by a mixed integer programming model. The algorithm, tested on realistic instances, shows a high reduction of the maximum space and a more regular warehouse saturation with negligible increase of the total cost. This paper, unlike other papers currently available in literature, provides instances data and results necessary for reproducibility, aiming to become a benchmark for future comparisons with other OICP algorithms

Reducing the clique and chromatic number via edge contractions and vertex deletions

We consider the following problem: can a certain graph parameter of some given graph G be reduced by at least d, for some integer d, via at most k graph operations from some specified set S, for some given integer k? As graph parameters we take the chromatic number and the clique number. We let the set S consist of either an edge contraction or a vertex deletion. As all these problems are NP-complete for general graphs even if d is fixed, we restrict the input graph G to some special graph class. We continue a line of research that considers these problems for subclasses of perfect graphs, but our main results are full classifications, from a computational complexity point of view, for graph classes characterized by forbidding a single induced connected subgraph H

Extensions of the minimum labelling spanning tree problem, Journal of Telecommunications and Information Technology, 2006, nr 4

In this paper we propose some extensions of the minimum labelling spanning tree problem. The main focus is on the minimum labelling Steiner tree problem: given a graph G with a color (label) assigned to each edge, and a subset Q of the nodes of G (basic vertices), we look for a connected subgraph of G with the minimum number of different colors covering all the basic vertices. The problem has several applications in telecommunication networks, electric networks, multimodal transportation networks, among others, where one aims to ensure connectivity by means of homogeneous connections. Numerical results for several metaheuristics to solve the problem are presented

Lipid peroxidation and total antioxidant capacity in vitreous, aqueous humor, and blood samples from patients with diabetic retinopathy

PurposeTo evaluate levels of malondialdehyde and the total antioxidant capacity (TAC) in the blood, aqueous humor, and vitreous bodies of diabetic and nondiabetic patients. We also measured the blood energy charge potential (ECP).MethodsWe examined 19 patients with type 2 diabetes mellitus and diabetic retinopathy. Ten were scheduled for cataract surgery and pars plana vitrectomy because of proliferative diabetic retinopathy (PDR). The other nine, with mild nonproliferative PDR (NPDR), and fourteen nondiabetic, age-matched subjects enrolled as a control group were scheduled for cataract surgery and vitrectomy because of epiretinal membranes. Blood, aqueous humor and vitreous body samples were collected at the time of surgery. Malondialdehyde concentrations and blood ECP were measured with high-performance liquid chromatography. The TAC of the samples was estimated with the oxygen radical absorbance capacity method.ResultsThe level of blood and vitreous malondialdehyde in the PDR group was significantly higher compared to controls and to NPDR patients. PDR patients also had lower levels of TAC at the vitreous body and aqueous humor level, but not at the blood level, compared to controls and with NPDR patients. In all diabetic patients, the blood ECP values were significantly lower, compared to control subjects.ConclusionsOur data support the hypothesis that oxidative stress and the decrease of antioxidant defenses are associated with the progression of diabetic retinopathy to its proliferative form. Antioxidant supply may have the effect of correcting oxidative stress and inhibiting disease progression

A linear time algorithm for the minimum Weighted Feedback Vertex Set on diamonds

Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in finding a subset Fsubset of or equal toV of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve WFVP on it

Minimum Weighted Feedback Vertex Set on Diamonds

Given a vertex weighted graph G, a minimum Weighted Feedback Vertex Set (MWFVS) is a subset F ? V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The MWFVS on general graph is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve MWFVS on it. We will discuss, moreover, how this result could be used to effectively improve the approximated solution of any known heuristic to solve MWFVS on a general graph

A Mathematical Programming Approach for the Maximum Labeled Clique Problem

This paper addresses a variant of the classical clique problem in which the edges of the graph are labeled. The problem consists of finding a clique as large as possible whose edge set contains at most b ∈ Z+ different labels. Moreover, in case of more feasible cliques of the same maximum size, we look for the one with the minimum number of labels. We study the time complexity of the problem, also in special cases, and we propose a mathematical programming approach for its solution by introducing two different formulations: the basic and the enforced. We experimentally evaluate the performance of the proposed approach on a set of benchmark instances (DIMACS) suitably adapted to the problem