Miklós Krész

Approximations of the Generalized Cascade Model

The study of infection processes is an important field of science both from the theoretical and the practical point of view, and has many applications. In this paper we focus on the popular Independent Cascade model and its generalization. Unfortunately the exact computation of infection probabilities is a #P-complete problem [8], so one cannot expect fast exact algorithms. We propose several methods to efficiently compute infection patterns with acceptable accuracy. We will also examine the possibility of substituting the Independent Cascade model with a computationally more tractable model.

Tutte type theorems for graphs having a perfect internal matching

Splitters are introduced to capture the meaning of barriers in graphs having a perfect internal matching. The factor-critical property is extended in a natural way to accommodate such graphs, and a characterization of factor-critical graphs is given in the new context. Two Tutte type theorems are presented for open graphs with perfect internal matchings, one on maximal splitters, and the other on maximal inaccessible splitters.

An Integrated Framework for Bus Logistics Management: Case Studies

This paper describes the most obvious way for public transportation companies to decrease their operational cost. This is to optimize the logistics of their operations. The optimization process is a very complex operation and therefore we split the logistics into three phases: vehicle scheduling, driver scheduling and driverrostering. The phases reflect also the split of a large problem (long term optimization) to the daily operation and finally to individual trips. The individual trips are then grouped into working shifts and to these are scheduled individual drivers. In the paper we present a detail description of bus scheduling. We use its mapping to the multiple depot vehicle scheduling problem (MDVSP) using a time-space network model. Finally, we solve the problem for two different cases – the city of Szeged and the city of Ljubljana.

Applications of the inverse infection problem on bank transaction networks

The Domingos-Richardson model, along with several other infection models, has a wide range of applications in prediction. In most of these, a fundamental problem arises: the edge infection probabilities are not known. To provide a systematic method for the estimation of these probabilities, the authors have published the Generalized Cascade Model as a general infection framework, and a learning-based method for the solution of the inverse infection problem. In this paper, we will present a case-study of the inverse infection problem. Bankruptcy forecasting, more precisely the prediction of company defaults is an important aspect of banking. We will use our model to predict these bankruptcies that can occur within a three months time frame. The network itself is built from the bank’s existing clientele for credit monitoring issues. We have found that using network models for short term prediction, we get much more accurate results than traditional scorecards can provide. We have also improved existing network models by using inverse infection methods for finding the best edge attribute parameters. This improved model was already implemented in August 2013 to OTP Banks credit monitoring process, and since then it has proven its usefulness.

The inverse infection problem

The applications of infection models like the Linear Threshold or the Domingos-Richardson model requires a graph weighted with infection probabilities. In many real-life applications these probabilities are unknown; therefore a systematic method for the estimation of these probabilities is required. One of the methods proposed to solve this problem, the Inverse Infection Model, was originally formulated for estimating credit default in banking applications. In this paper we are going to test the capabilities of the Inverse Infection Model in a more controlled environment. We are going to use artificially created graphs to evaluate the speed and the accuracy of estimations. We are also going to examine how approximations and heuristics can be used to improve the speed of the calculations. Finally, we will experiment with the amount of a priori information available in the model and evaluate how well this method performs if only partial information is available.

An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.

Dynamic communities and their detection

Overlapping community detection has already become an interesting problem in data mining and also a useful technique in applications. This underlines the importance of following the lifetime of communities in real graphs. Palla et al. developed a promising method, and analyzed community evolution on two large databases [23]. We have followed their footsteps in analyzing large real-world databases and found, that the framework they use to describe the dynamics of communities is insufficient for our data. The method used by Palla et al. is also dependent on a very special community detection algorithm, the clique percolation method, and on its monotonic nature. In this paper we propose an extension of the basic community events described in [23] and a method capable of handling communities found a nonmonotonic community detection algorithm. We also report on findings that came from the tests on real social graphs.

A Depth-first Algorithm to Reduce Graphs in Linear Time

A redex in a graph G is a triple r=(u,c,v) of distinct vertices that determine a 2-star. Shrinking r means deleting the center c and merging u with v intoone vertex. Reduction of G entails shrinking all of its redexes in a recursive way, and, at the same time, deleting all loops that are created during this process. It is shown that reduction can be implemented in O(m)time, where m is the number of edges in G.

Application Oriented Variable Fixing Methods for the Multiple Depot Vehicle Scheduling Problem

In this article, we present heuristic methods for the vehicle scheduling problem that solve it by reducing the problem size using different variable fixing approaches. These methods are constructed in a way that takes some basic driver requirements into consideration as well. We show the efficiency of the methods on real-life and random data instances too. We also give an improved way of generating random input for the vehicle scheduling problem.

Soliton automata with constant external edges

Soliton automata are the mathematical models of certain possible molecular switching devices. Both from theoretical and practical point of view, it is a central question to describe soliton automata with constant external edges. Extending a result of Dassow and Jurgensen, we characterize soliton automata in this special case.