A new mixed integer linear programming formulation for the maximum degree bounded connected subgraph problem

Maksimović, Zoran Lj.

doi:10.2298/pim1613099m

Cited by 6 publications

(1 citation statement)

References 17 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another important element of our ILP model for the separation of congruent-2k3 cycle inequalities is the connectivity constraints, which we formulate exploiting the ideas presented in [26], by setting a network flow model. Given the original graph G = (V, E) the flow networks is defined as H = (V, A),…”

mentioning

confidence: 99%

Total Coloring and Total Matching: Polyhedra and Facets

Ferrarini¹,

Gualandi²

2021

Preprint

View full text Add to dashboard Cite

A total coloring of a graph G = (V, E) is an assignment of colors to vertices and edges such that neither two adjacent vertices nor two incident edges get the same color, and, for each edge, the end-points and the edge itself receive different colors. Any valid total coloring induces a partition of the elements of G into total matchings, which are defined as subsets of vertices and edges that can take the same color. In this paper, we propose Integer Linear Programming models for both the Total Coloring and the Total Matching problems, and we study the strength of the corresponding Linear Programming relaxations. The total coloring is formulated as the problem of finding the minimum number of total matchings that cover all the graph elements, and we prove that this relaxation is tighter than a natural assignment model. This covering formulation can be solved by a column generation algorithm, where the pricing subproblem corresponds to the Weighted Total Matching Problem. Hence, we study the Total Matching Polytope. We introduce two families of nontrivial valid inequalities: congruent-2k3 cycle inequalities based on the parity of the vertex set induced by the cycle, and clique inequalities induced by complete subgraphs of even order. We prove that congruent-2k3 cycle inequalities are facet-defining only when k = 4, while the even cliques are always facet-defining. Since the separation problem of the clique inequalities of even order is NP-hard, we get a polyhedral proof of the NP-hardness of the Weighted Total Matching Problem.

show abstract

mentioning

confidence: 99%

Total Coloring and Total Matching: Polyhedra and Facets

Ferrarini¹,

Gualandi²

2021

Preprint

View full text Add to dashboard Cite

show abstract

Determining critical nodes in optimal cost attacks on networked infrastructures

Ahmad,

Clark,

Ali

et al. 2024

Discov Internet Things

View full text Add to dashboard Cite

A wide range of critical infrastructures are connected via wide area networks as well as the Internet-of-Thing (IoT). Apart from natural disasters, these infrastructures, providing services such as electricity, water, gas, and Internet, are vulnerable to terrorist attacks. Clearly, damages to these infrastructures can have dire consequences on economics, health services, security and safety, and various business sectors. An infrastructure network can be represented as a directed graph in which nodes and edges denote operation entities and dependencies between entities, respectively. A knowledgeable attacker who plans to harm the system would aim to use the minimum amount of effort, cost, or resources to yield the maximum amount of damage. Their best strategy would be to attack the most critical nodes of the infrastructure. From the defender’s side, the strategy would be to minimize the potential damage by investing resources in bolstering the security of the critical nodes. Thus, in the struggle between the attacker and defender, it becomes important for both the attacker and defender to identify which nodes are most critically significant to the system. Identifying critical nodes is a complex optimization problem. In this paper, we first present the problem model and then propose a solution for computing the optimal cost attack while considering the failure propagation. The proposed model represents one or multiple interconnected infrastructures. While considering the attack cost of each node, the proposed method computes the optimal attack that a rational attacker would make. Our problem model simulates one of two goals: maximizing the damage for a given attack budget or minimizing the cost for a given amount of damage. Our technique obtains solutions to optimize the objective functions by utilizing integer-linear programming while observing the constraints for each of the specified goals. The paper reports an extensive set of experiments using various graphs. The results show the efficacy of our technique in terms of its ability to obtain solutions with fast turnaround times.

show abstract