Resolvable Networks—A Graphical Tool for Representing and Solving SAT

In this paper, we introduce the notion of resolvable networks. A resolvable network is a digraph of subnetworks, where subnetworks may overlap, and the inner structure of subnetworks are not interesting from the viewpoint of the network. There are two special subnetworks, Source and Sink, with the following properties: there is no incoming edge to Source, and there is no outgoing edge from Sink. Any resolvable network can be represented by a satisfiability problem in Boolean logic (shortly, SAT problem), and any SAT problem can be represented by a resolvable network. Because of that, the resolution operation is valid also for resolvable networks. We can use resolution to find out or refine the inner structure of subnetworks. We give also a pessimistic and an optimistic interpretation of subnetworks. In the pessimistic case, we assume that inside a subnetwork, all communication possibilities are represented as part of the resolvable network. In the optimistic case, we assume that each subnetwork is strongly connected. We show that any SAT problem can be visualized using the pessimistic interpretation. We show that transitivity is very limited in the pessimistic interpretation, and in this case, transitivity corresponds to resolution of clauses. In the optimistic interpretation of subnetworks, we have transitivity without any further condition, but not all SAT problems can be represented in this case; however, any such network can be represented as a SAT problem. The newly introduced graphical concept allows to use terminology and tools from directed graphs in the field of SAT and also to give graphical representations of various concepts of satisfiability problems. A resolvable network is also a suitable data structure to study, for example, wireless sensor networks. The visualization power of resolvable networks is demonstrated on some pigeon hole SAT problems. Another important application field could be modeling the communication network of an information bank. Here, a subnetwork represents a dataset of a user which is secured by a proxy. Any communication should be done through the proxy, and this constraint can be checked using our model.

A new strategy for synchronizing traffic flow on a distributed simulation using SUMO

The Project Modelling and Control of Urban Traffic in the City of Medell ́ın (MOY- COT) has produced multiple results in modelling, simulation and control of multimodal urban traffic using the SUMO simulator. As the simulations became more complex the necessity to distribute the computational load rose. Therefore, an approach for network partitioning and border edges management was introduced. In this paper a new border edge management strategy is presented for distributed simulation with SUMO. Unlike the previous approaches, which were developed in Python programming language using the corresponding TraCI client and tools such as sumolib, the strategy presented in this work was developed in C++ using the TraCI client for this language. Additionally, this strategy involves a simplified process for network partitioning since the border edges are preserved in every partition, without the need of splitting them. In this case, neighboring partitions behave in a master-slave fashion, depending on whether the border edge is an incoming edge or an outgoing edge. Concretely, a given partition is a master for its incoming edges and a slave for its outgoing ones. Furthermore, all the vehicles are found in the master and the slave partitions, where the master partition controls its slaves through the TraCI commands slowDown and moveTo that correct the position of these vehicles. Simulation results show that this new strategy presents better precision than the previous one. The description of the new procedure for border edge management is detailed. Finally, it is compared with the previous approach and the non-distributed simulation using a free flow scenario and a scenario with queue formation is presented.