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The original formulation of the firefighter problem defines a discrete-time process where a fire starts at a designated subset of the vertices of a graph G. At each subsequent discrete time unit, the fire propagates from each burnt vertex to all of its neighbors unless they are defended by a firefighter that can move between any pair of vertices in a single time unit. Once a vertex is burnt or defended, it remains in that state, and the process terminates when the fire can no longer spread. In this work, we present the moving firefighter problem, which is a generalization of the firefighter problem where the time it takes a firefighter to move from a vertex u to defend vertex v is determined by a function τ. This new formulation models situations such as a wildfire or a flood, where firefighters have to physically move from their current position to the location of an entity they intend to defend. It also incorporates the notion that entities modeled by the vertices are not necessarily instantaneously defended upon the arrival of a firefighter. We present a mixed-integer quadratically constrained program (MIQCP) for the optimization version of the moving firefighter problem that minimizes the number of burnt vertices for the case of general finite graphs, an arbitrary set F ⊂ V of vertices where the fire breaks out, a single firefighter, and metric time functions τ. [ABSTRACT FROM AUTHOR]

The specification and formal verification of distributed systems is usually a complex task. It requires extensive knowledge of algorithm theory and modeling of distributed or concurrent systems. In this context, we present LeGESD which is a framework oriented to support the specification and formal validation of concurrent and distributed systems. LeGESD has a graphical formal language for the specification and analysis of distributed systems which is used to describe functional and of communication requirements. The semantics of LeGESD is based on the process algebra. This semantics is also described in this paper and it is called Analysis and Design of Distributed Systems (ADSD). ADSD is an algebraic specification with operational semantics defined to be used with LeGESD. ADSD provides graphical-algebraic equivalence relations which can be used to generate formal specifications of distributed systems. Lastly, this paper presents an example which shows the usefulness and potential of the language and its semantics. [ABSTRACT FROM AUTHOR]

The capacitated vertex k-center problem receives as input a complete weighted graph and a set of capacity constraints. Its goal is to find a set of k centers and an assignment of vertices that does not violate the capacity constraints. Furthermore, the distance from the farthest vertex to its assigned center has to be minimized. The capacitated vertex k-center problem models real situations where a maximum number of clients must be assigned to centers and the travel time or distance from the clients to their assigned center has to be minimized. These centers might be hospitals, schools, police stations, among many others. The goal of this paper is to explicitly state how the capacitated vertex k-center problem and the minimum capacitated dominating set problem are related. We present an exact algorithm that consists of solving a series of integer programming formulations equivalent to the minimum capacitated dominating set problem over the bottleneck input graph. Lastly, we present an empirical evaluation of the proposed algorithm using off-the-shelf optimization software. [ABSTRACT FROM AUTHOR]