A. Ridha Mahjoub

Short Communication: Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval

In a recent paper [Theoretical Computer Science 363, 257-265], He, Zhong and Gu considered the non-resumable case of the scheduling problem with a fixed non-availability interval under the non-resumable scenario. They proposed a polynomial time approximation scheme (PTAS) to minimize the total completion time. In this paper, we propose a fully polynomial-time approximation scheme to minimize the total weighted completion time. The FPTAS has O(n^2/@e^2) time complexity, where n is the number of jobs and @e is the required error bound. The proposed FPTAS outperforms all the previous approximation algorithms designed for this problem and its running time is strongly polynomial.

On the k edge-disjoint 2-hop-constrained paths polytope

The k edge-disjoint 2-hop-constrained paths problem consists in finding a minimum cost subgraph such that between two given nodes s and t there exist at least k edge-disjoint paths of at most 2 edges. We give an integer programming formulation for this problem and characterize the associated polytope.

Solving VLSI design and DNA sequencing problems using bipartization of graphs

In this paper we consider the 2-layer constrained via minimization problem and the SNP haplotype assembly problem. The former problem arises in the design of integrated and printed circuit boards, and the latter comes up in the DNA sequencing process for diploid organisms. We show that, for any maximum junction degree, the problem can be reduced to the maximum bipartite induced subgraph problem. Moreover we show that the SNP haplotype assembly problem can also be reduced to the maximum bipartite induced subgraph problem for the so-called minimum error correction criterion. We give a partial characterization of the bipartite induced subgraph polytope. Using this, we devise a branch-and-cut algorithm and report some experimental results. This algorithm has been used to solve real and large instances.

Hop‐level flow formulation for the survivable network design with hop constraints problem

The hop-constrained survivable network design problem consists of finding a minimum cost subgraph containing K edge-disjoint paths with length at most H joining each pair of vertices in a given demand set. When all demands have a common vertex, the instance is said to be rooted. We propose a new extended formulation for the rooted case, called hop-level multicommodity flow (MCF), that can be significantly stronger than the previously known formulations, at the expense of having a larger number of variables and constraints, growing linearly with the number of edges and demands and quadratically with H. However, for the particular case where H = 2, it can be specialized into a very compact and efficient formulation. Even when H = 3, hop-level-MCF can still be quite efficient and it has solved several instances from the literature for the first time.

On the NP-completeness of the perfect matching free subgraph problem

Given a bipartite graph G=(U@?V,E) such that |U|=|V| and every edge is labelled true or false or both, the perfect matching free subgraph problem is to determine whether or not there exists a subgraph of G containing, for each node u of U, either all the edges labelled true or all the edges labelled false incident to u, and which does not contain a perfect matching. This problem arises in the structural analysis of differential-algebraic systems. The purpose of this paper is to show that this problem is NP-complete. We show that the problem is equivalent to the stable set problem in a restricted case of tripartite graphs. Then we show that the latter remains NP-complete in that case. We also prove the NP-completeness of the related minimum blocker problem in bipartite graphs with perfect matching.

The Maximum Induced Bipartite Subgraph Problem with Edge Weights

Given a graph

A New Risk Assessment Framework Using Graph Theory for Complex ICT Systems

G=(V,E)

Two node‐disjoint hop‐constrained survivable network design and polyhedra

with nonnegative weights on the edges, the maximum induced bipartite subgraph problem (MIBSP) is to find a maximum weight bipartite subgraph

Survivability in Hierarchical Telecommunications Networks Under Dual Homing

(W,E[W])

Generating Facets for the Independence System Polytope

of