Recognizing near-bipartite Pfaffian graphs in polynomial time

A matching covered graph is a non-trivial connected graph in which every edge is in some perfect matching. A non-bipartite matching covered graph G is near-bipartite if there are two edges e₁ and e₂ such that G−e₁−e₂ is bipartite and matching covered. In 2000, Fischer and Little characterized Pfaffian near-bipartite graphs in terms of forbidden subgraphs [I. Fischer, C.H.C. Little, A characterization of Pfaffian near bipartite graphs, J. Combin. Theory Ser. B 82 (2001) 175-222.]. However, their characterization does not imply a polynomial time algorithm to recognize near-bipartite Pfaffian graphs. In this article, we give such an algorithm.We define a more general class of matching covered graphs, which we call weakly near-bipartite graphs. This class includes the near-bipartite graphs. We give a polynomial algorithm for recognizing weakly near-bipartite Pfaffian graphs. We also show that Fischer and Little’s characterization of near-bipartite Pfaffian graphs extends to this wider class.     

Adaptive and multi-mining versions of the DM-GRASP hybrid metaheuristic

Metaheuristics represent an important class of techniques to solve, approximately, hard combinatorial optimization problems for which the use of exact methods is impractical. Some researches have been combining machine learning techniques with metaheuristics to adaptively guide and improve the search for near optimal solutions. An example of such development is the DM-GRASP, a hybrid version of the Greedy Randomized Adaptative Search Procedures (GRASP) metaheuristic which incorporates a data mining process. In this hybrid proposal, after executing half of the total number of iterations, the data mining process extracts patterns from an elite set of sub-optimal solutions for the optimization problem. These patterns present characteristics of near optimal solutions and can be used to guide the following half GRASP iterations in the search through the solution space. In this work, we explore new versions of the DM-GRASP metaheuristic to experiment, not a single activation, but multiple and adaptive executions of the data mining process during the metaheuristic execution. We also applied the data mining technique into a reactive GRASP to show that a more sophisticated and not memoryless GRASP approach can also benefit from the use of this technique. In order to evaluate these new proposals, we adopted the server replication for reliable multicast problem since the best known results for this problem were obtained by GRASP and DM-GRASP implementations. The computational experiments, comparing traditional GRASP, DM-GRASP, and the new proposals, showed that multiple and adaptive executions of the data mining process can improve the results obtained by the DM-GRASP hybrid metaheuristic—the new proposals were able to find better results in less computational time for the reliable multicast problem.     

On multiplicities of simple subquotients in generalized Verma modules

We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.     

Strategic arrivals to queues offering priority service

Queueing Systems - We consider strategic arrivals to a FCFS service system that starts service at a fixed time and has to serve a fixed number of customers, for example, an airplane boarding...     

Deformations and transversality of pseudo-holomorphic discs

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudoholomorphic discs form a Banach manifold.     

Timed Petri nets and prediction to improve the Chandy–Misra conservative-distributed simulation

The main contribution of this paper shows that distributed simulation of timed Petri nets (TPN) can take advantage of their structure to obtain a significant lookahead which is usually difficult to compute with other models. In this paper, we introduce a conservative-distributed simulation with a reduced number of control messages and without deadlock resolution. This approach is based on a part of optimism computed on the prediction time each logical process can determine for its advancement. Obviously this prediction time must be computed easily according to the structure of the simulated logical process. Timed Petri nets meet these requirements and we use their structure to evaluate the depth of the prediction. In conservative-distributed simulation, it is known that the deeper the prediction, the better the efficiency of the simulation. We present a method we have devised based on channel time prediction. We compare its performance to the Chandy–Misra method and to some related Petri nets approaches (Chiola). Experiments carried out on Sun stations show that there is more parallelism and a reduced number of null messages in the cases of deadlock avoidance. Moreover, considering deadlock detection and resolution technique we observe that in many cases no deadlock occurs with less control messages.     

Almost continuous orbit equivalence for non-singular homeomorphisms

Let X and Y be Polish spaces with non-atomic Borel measures μ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, μ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III ₁ or that they are both of type III _λ, 0 < λ < 1 and, in the III _λ case, suppose in addition that both ‘topological asymptotic ranges’ (defined in the article) are log λ · ℤ. Then there exist invariant dense G _δ-subsets X′ ⊂ X and Y′ ⊂ Y of full measure and a non-singular homeomorphism ϕ: X′ → Y′ which is an orbit equivalence between T| _X′ and S| _Y′, that is ϕ{T ⁱ x} = {S ⁱ ϕx} for all x ∈ X′. Moreover, the Radon-Nikodym derivative dν ∘ ϕ/dμ is continuous on X′ and, letting S′ = ϕ ⁻¹ Sϕ, we have T _x = S′ ^n(x) x and S′x = T ^m(x) x where n and m are continuous on X′.