We consider a game that was played in a German television show that is similar to the sorting balls puzzle. In it, we are assumed to move one colored ball after another in a set of colored tubes so that in the end, each ball is in the tube of its color. We are allowed to use one additional (uncolored) tube. We show general properties for solvability and that the problem of minimizing the number of moves is NP-hard, which is done by a reduction from the Feedback Arc Set Problem. Furthermore, we give an implementation of an algorithm to compute such a minimal sequence of moves. The algorithm is based on breadth-first search and accelerated by a lower bound on the number of moves from the current configuration to the final one that is obtained by solving a small instance of the Feedback Arc Set Problem. Our experiments show that instances with 7 colored tubes of height 4 can be solved in a reasonable amount of time and that the number of tubes is much more critical for the running time than the heights of the tubes.

Differentially private ML approaches seek to learn models which may be publicly released while guaranteeing that the input data is kept private. One issue with this construction is that further model releases based on the same training data (e.g. for a new task) incur a further privacy budget cost. Privacy-preserving synthetic data generation is one possible solution to this conundrum. However, models trained on synthetic private data struggle to approach the performance of private, ad-hoc models. In this paper, we present a novel method based on sum-product networks that is able to perform both privacy-preserving classification and privacy-preserving data generation with a single model. To the best of our knowledge, ours is the first approach that provides both discriminative and generative capabilities to differentially private ML. We show that our approach outperforms the state of the art in terms of stability (i.e. number of training runs required for convergence) and utility of the generated data.

Solid State Drives (SSDs) have replaced magnetic disks in many application areas, as they provide very high performance for arbitrary access patterns. Nevertheless, data written to a physical page has to be erased before a page can be rewritten. The corresponding garbage collection (GC) process can only be performed on a block granularity, where a block includes many pages, impacting both the performance and lifetime of an SSD. The cost of a GC process is typically measured in terms of its write amplification, i.e., the number of blocks internally written by the SSD divided by the number of write requests of the host.Several GC heuristics have been proposed to optimize the write amplification of SSDs. These heuristics have been mostly empirically evaluated, while no thorough theoretical results are available on the optimality of GC algorithms even for seemingly simple cases like uniform and independent access distributions.In this work, we theoretically investigate the GREEDY GC strategy for uniformly independently distributed write accesses. We therefore model the garbage collection process on SSDs as a stochastic process and prove that the expected write amplification incurred by the GREEDY GC strategy is at most that of any other online GC strategy.

Computing the shortest path in a road network is a fundamental problem that has attracted lots of attention. However, in many real-world scenarios, determining solely the shortest path is not enough as users want to have additional, alternative ways of reaching their destination. In this paper, we investigate a novel variant of alternative routing, termed the k-Most Diverse Near-Shortest Paths (kMDNSP). In contrast to previous work, kMDNSP aims at maximizing the diversity of the recommended paths, while bounding their length based on a user-defined constraint. Our theoretical analysis proves the NP-hardness of the problem at hand. To compute an exact solution to kMDNSP, we present an algorithm which iterates over all paths that abide by the length constraint and generates k-subsets of them as candidate results. Furthermore, in order to achieve scalability, we also design three heuristic algorithms that trade the diversity of the result for performance. Our experimental analysis compares all proposed algorithms in terms of their runtime and the quality of the recommended paths.

We revisit the exact algorithm to compute the treewidth of a graph of Tamaki and present it in a way that facilitates improvements. The so-called I-blocks and O-blocks enumerated by the algorithm are interpreted as subtrees of a tree-decomposition that is constructed. This simplifies the proof of correctness and allows to discard subtrees from the enumeration by some simple observations. In our experiments, we show that one of these modifications in particular reduces the number of enumerated objects considerably.

Craig interpolation has turned out to be an essential method for many applications in formal verification. In this paper we focus on the computation of simple interpolants for the theory of linear arithmetic with rational coefficients. We successfully minimize the number of linear constraints in the final interpolant by several methods including proof transformations, linear programming, and SMT solving. Experimental results comparing the approach to standard methods from the literature prove the effectiveness of the approach and show reductions of up to 70% in the number of linear constraints.

Hard real-time systems require tasks to finish in time. To guarantee the timeliness of such a system, static timing analyses derive upper bounds on the worst-case execution time (WCET) of tasks. There are two types of timing analyses: numeric and parametric. A numeric analysis derives a numeric timing bound and, to this end, assumes all information such as loop bounds to be given a priori. If these bounds are unknown during analysis time, a parametric analysis can compute a timing formula parametric in these variables. A performance bottleneck of timing analyses, numeric and especially parametric, is the so-called path analysis, which determines the path in the analyzed task with the longest execution time bound.In this paper, we present a new approach to path analysis. This approach exploits the often rather regular structure of software for hard real-time and safety-critical systems. As we show in the evaluation of this paper, we strongly improve upon former techniques in terms of precision and runtime in the parametric case. Even in the numeric case, the approach competes with state-of-the-art techniques and may be an alternative to commercial tools employed for path analysis.

BACKGROUND: Protein conformation and protein/protein interaction can be elucidated by solution-phase Hydrogen/Deuterium exchange (sHDX) coupled to high-resolution mass analysis of the digested protein or protein complex. In sHDX experiments mutant proteins are compared to wild-type proteins or a ligand is added to the protein and compared to the wild-type protein (or mutant). The number of deuteriums incorporated into the polypeptides generated from the protease digest of the protein is related to the solvent accessibility of amide protons within the original protein construct. RESULTS: In this work, sHDX data was collected on a 14.5 T FT-ICR MS. An algorithm was developed based on combinatorial optimization that predicts deuterium exchange with high spatial resolution based on the sHDX data of overlapping proteolytic fragments. Often the algorithm assigns deuterium exchange with single residue resolution. CONCLUSIONS: With our new method it is possible to automatically determine deuterium exchange with higher spatial resolution than the level of digested fragments.

We establish stability results for a class of biological networks with different time-scales under parameter perturbations and determine conditions that ensure the existence of exponentially stable equilibria of the perturbed biological system. The perturbed system is modelled as nonlinear perturbations to a known nonlinear idealized system and is represented by two time-scale subsystems. We derive a Lyapunov function for the coupled system and a maximal upper bound for the fast time scale associated with the fast state. Resulting stability conditions for two important biological networks, a neural network and a gene regulatory network are derived.

We present the first algorithm that computes optimal orderings of sentences into a locally coherent discourse. The algorithm runs very efficiently on a variety of coherence measures from the literature. We also show that the discourse ordering problem is NP-complete and cannot be approximated.

We study the problem of assigning transmission ranges to the nodes of ad hoc wireless networks to minimize power consumption while ensuring network connectivity. We give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35-40 nodes in 1 hour; a proof that min-power symmetric connectivity with asymmetric power requirements is inapproximable within factor (1 - /spl epsi/) ln |V| for any /spl epsi/ > 0 unless P = NP; an improved analysis for two approximation algorithms recently proposed by Calinescu et al. (TCS'02), decreasing the best known approximation factor to 5/3 + /spl epsi/; and a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.

An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves $\gamma$. The task is to connect the points in V in the order in which they lie on $\gamma$. Giesen [Proceedings of the 15th Annual ACM Symposium on Computational Geometry (SCG '99), 1999, pp. 207--216] showed recently that the traveling salesman tourof V solves the reconstruction problem for single closed curves under otherwise weak assumptions on $\gamma$ and V; $\gamma$ must be a single closed curve. We extend his result along several directions: we weaken the assumptions on the sample; we show that traveling salesman-based reconstruction also works for single open curves (with and without specified endpoints) and for collections of closed curves; we give alternative proofs; and we show that in the context of curve reconstruction, the traveling salesman tour can be constructed in polynomial time.