The Missing Mass Problem

We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally bounded metric spaces that may be of independent interest.Comment: 15 page

Effect of Initial Assignment on Local Search Performance for Max Sat

In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows

The Time for Reconstructing the Attack Graph in DDoS Attacks

Despite their frequency, denial-of-service (DoS\blfootnote{Denial of Service (DoS), Distributed Denial of Service (DDoS), Probabilistic Packet Marking (PPM), coupon collector's problem (CCP)}) and distributed-denial-of-service (DDoS) attacks are difficult to prevent and trace, thus posing a constant threat. One of the main defense techniques is to identify the source of attack by reconstructing the attack graph, and then filter the messages arriving from this source. One of the most common methods for reconstructing the attack graph is Probabilistic Packet Marking (PPM). We focus on edge-sampling, which is the most common method. Here, we study the time, in terms of the number of packets, the victim needs to reconstruct the attack graph when there is a single attacker. This random variable plays an important role in the reconstruction algorithm. Our main result is a determination of the asymptotic distribution and expected value of this time. The process of reconstructing the attack graph is analogous to a version of the well-known coupon collector's problem (with coupons having distinct probabilities). Thus, the results may be used in other applications of this problem.Comment: 31 pages, 5 figures, 1 tabl

Operational behaviour of graded diamond grinding wheels for end mill cutter machining

The varying related material removal rate during deep grinding of cemented carbide end mill cutters results in an unevenly wear of the grinding wheel. This study therefore presents a simulation-based model for the load-adjusted design of grinding wheels to achieve balanced radial wear, as well as an evaluation of this model. The related material removal rate along the width of the grinding wheel is determined by a Dexel based material removal simulation for different end mill geometries. Based on these results an equation is derived to adapt the abrasive layer properties to the local load differences. Three grinding wheels with different types of gradients are then manufactured by a grinding tool manufacturer based on this equation. These and two grinding wheels with constant abrasive layer properties are used for deep grinding of ten end mills each. Afterwards the radial wear of each grinding wheel is measured by a confocal microscope. An analysis of the cutting edge chipping is done to evaluate the influence on the graded grinding wheels on the cutting edge quality. It was found that a reduction of the wear difference over the grinding wheel width of 52% and an improved cutting edge quality can be achieved by using graded grinding tools. This allows the time intervals between dressing steps to be increased without compromising the accuracy of the grinding process, thus also increasing its productivity. Finally, this article shows that the presented model allows for a more balanced wear behaviour, but has to be extended by considering further factors influencing radial wear

Dressing of hybrid-bonded graded diamond grinding wheels

For tool grinding, an optimization potential in terms of productivity is available using graded grinding wheels. This is especially the case when grinding flutes in cemented carbide. Due to the properties of the cemented carbide, high radial wear occurs. Depending on the geometry of the flute, the radial wear varies along the engagement width of the grinding tool. The varying radial wear can be compensated by load adapting the grinding tool properties along its engagement width. The adaptation of the wear behaviour to non-uniform engagement conditions results in non-uniform radial wear occurring under uniform engagement conditions. Indeed, this is the case when dressing these grinding tools. Therefore, this publication presents a method that enables the dressing of graded grinding wheels. For this purpose, four differently graded grinding wheels and two non-graded grinding wheels are dressed with SiC-rolls. Different SiC-rolls, as well as dressing parameters, are investigated. The contour accuracy after dressing is analysed using contour profiles in polyurethane. In the presented paper, dressing parameters are proposed which allow reproducible dressing of all grinding wheels used