arXiv subjects

Jörg-Rüdiger Sack

Publications and source records attributed to Jörg-Rüdiger Sack.

11 recordsLinked to original sources

arXiv2026

Enumerating Length-Bounded Simple Paths and Cycles in Directed Graphs with $O(k(n+m))$ Delay Using Edge-Consistent Node Barriers

Enumerating simple paths and cycles subject to a given length bound is a fundamental problem in graph algorithms. Recent algorithms, namely BC-DFS (Peng et al. 2019, 2021) and CYCLE_SEARCH (Gupta and Suzumura 2021, arXiv:2105.10094v2), employ cached barrier values to prune fruitless searches. Both algorithms turn out to produce incomplete output, and their delay-bound arguments rely on flawed claims. For CYCLE_SEARCH this is known (arXiv:2512.08392); here we establish the analogous results for BC-DFS by exhibiting graphs on which paths are missed, by identifying the defect in its barrier-update procedure, and by refuting the monotonicity claim on which its delay-bound proof rests. As our main contribution, we introduce edge-consistency, a local invariant on barrier values analogous to heuristic consistency in informed search. It provides an incremental mechanism for maintaining admissible barrier estimates and yields concise correctness proofs. We use edge-consistency as a unifying framework for design and analysis of Bounded-Scope Depth-First Search (BS-DFS) --- a new algorithm for enumerating simple paths or cycles of length at most $k$ in a directed graph. For BS-DFS we prove a worst-case delay of at most $3(k+1)(n+m)$ elementary steps between consecutive events (start, each output, termination) and an amortized delay of at most $2(k+1)(n+m)$ steps per event, the $p$-th event being reached within $2p(k+1)(n+m)$ steps; both bounds are in $O(k(n+m))$. Barrier admissibility alone is not sufficient for the delay bound: for two variants with simpler barrier management, we exhibit a graph family forcing $\Omega(k^2(n+m))$ delay between outputs. Experiments on two families of random graphs confirm our findings, support the significance of the incompleteness result, and show that achieving completeness has modest empirical cost.

cs.DS↗

arXiv2025

Finding All Bounded-Length Simple Cycles in a Directed Graph -- Revisited

In 2021, Gupta and Suzumura proposed a novel algorithm for enumerating all bounded-length simple cycles in directed graphs (arXiv:2105.10094). In this work, we present a concrete counter-example demonstrating that the proposed algorithm fails to enumerate certain valid cycles. Analyzing it, we pinpoint the precise step at which the original correctness proof breaks down. We also identify a gap in the original proof of the delay bound claimed. Finally, we propose algorithm SimpleSearch avoiding these flaws by construction, while achieving the delay bound $O(k(n + m))$ per cycle output or termination; where $k$ is the length bound, $n$ the number of nodes, and $m$ the number of edges in the finite simple directed graph $G$.

cs.DS↗

arXiv2022

Predicting the Citation Count and CiteScore of Journals One Year in Advance

Prediction of the future performance of academic journals is a task that can benefit a variety of stakeholders including editorial staff, publishers, indexing services, researchers, university administrators and granting agencies. Using historical data on journal performance, this can be framed as a machine learning regression problem. In this work, we study two such regression tasks: 1) prediction of the number of citations a journal will receive during the next calendar year, and 2) prediction of the Elsevier CiteScore a journal will be assigned for the next calendar year. To address these tasks, we first create a dataset of historical bibliometric data for journals indexed in Scopus. We propose the use of neural network models trained on our dataset to predict the future performance of journals. To this end, we perform feature selection and model configuration for a Multi-Layer Perceptron and a Long Short-Term Memory. Through experimental comparisons to heuristic prediction baselines and classical machine learning models, we demonstrate superior performance in our proposed models for the prediction of future citation and CiteScore values.

cs.DL↗

arXiv2021

Obfuscation of Images via Differential Privacy: From Facial Images to General Images

Due to the pervasiveness of image capturing devices in every-day life, images of individuals are routinely captured. Although this has enabled many benefits, it also infringes on personal privacy. A promising direction in research on obfuscation of facial images has been the work in the k-same family of methods which employ the concept of k-anonymity from database privacy. However, there are a number of deficiencies of k-anonymity that carry over to the k-same methods, detracting from their usefulness in practice. In this paper, we first outline several of these deficiencies and discuss their implications in the context of facial obfuscation. We then develop a framework through which we obtain a formal differentially private guarantee for the obfuscation of facial images in generative machine learning models. Our approach provides a provable privacy guarantee that is not susceptible to the outlined deficiencies of k-same obfuscation and produces photo-realistic obfuscated output. In addition, we demonstrate through experimental comparisons that our approach can achieve comparable utility to k-same obfuscation in terms of preservation of useful features in the images. Furthermore, we propose a method to achieve differential privacy for any image (i.e., without restriction to facial images) through the direct modification of pixel intensities. Although the addition of noise to pixel intensities does not provide the high visual quality obtained via generative machine learning models, it offers greater versatility by eliminating the need for a trained model. We demonstrate that our proposed use of the exponential mechanism in this context is able to provide superior visual quality to pixel-space obfuscation using the Laplace mechanism.

cs.CR↗

arXiv2020

Differential Privacy Via a Truncated and Normalized Laplace Mechanism

When querying databases containing sensitive information, the privacy of individuals stored in the database has to be guaranteed. Such guarantees are provided by differentially private mechanisms which add controlled noise to the query responses. However, most such mechanisms do not take into consideration the valid range of the query being posed. Thus, noisy responses that fall outside of this range may potentially be produced. To rectify this and therefore improve the utility of the mechanism, the commonly used Laplace distribution can be truncated to the valid range of the query and then normalized. However, such a data-dependent operation of normalization leaks additional information about the true query response thereby violating the differential privacy guarantee. Here, we propose a new method which preserves the differential privacy guarantee through a careful determination of an appropriate scaling parameter for the Laplace distribution. We also generalize the privacy guarantee in the context of the Laplace distribution to account for data-dependent normalization factors and study this guarantee for different classes of range constraint configurations. We provide derivations of the optimal scaling parameter (i.e., the minimal value that preserves differential privacy) for each class or provide an approximation thereof. As a consequence of this work, one can use the Laplace distribution to answer queries in a range-adherent and differentially private manner.

cs.DB↗

arXiv2019

A New Model in Firefighting Theory

Continuous and discrete models for firefighting problems are well-studied in Theoretical Computer Science. We introduce a new, discrete, and more general framework based on a hexagonal cell graph to study firefighting problems in varied terrains. We present three different firefighting problems in the context of this model; for two of which, we provide efficient polynomial time algorithms and for the third, we show NP-completeness. We also discuss possible extensions of the model and their implications on the computational complexity.

cs.CG↗

arXiv2018

Rectilinear Shortest Paths Among Transient Obstacles

This paper presents an optimal $Θ(n \log n)$ algorithm for determining time-minimal rectilinear paths among $n$ transient rectilinear obstacles. An obstacle is transient if it exists in the scene only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among transient rectilinear obstacles and a pair of points $s$, $d$, we determine a time-minimal, obstacle-avoiding path from $s$ to $d$. The main challenge in solving this problem arises as the robot may be required to wait for an obstacle to disappear, before it can continue moving toward the destination. Our algorithm builds on the continuous Dijkstra paradigm, which simulates propagating a wavefront from the source point. We also solve a query version of this problem. For this, we build a planar subdivision with respect to a fixed source point, so that minimum arrival time to any query point can be reported in $O(\log n)$ time, using point location for the query point in this subdivision.

cs.CG↗

arXiv2018

Time-Dependent Shortest Path Queries Among Growing Discs

The determination of time-dependent collision-free shortest paths has received a fair amount of attention. Here, we study the problem of computing a time-dependent shortest path among growing discs which has been previously studied for the instance where the departure times are fixed. We address a more general setting: For two given points $s$ and $d$, we wish to determine the function $\mathcal{A}(t)$ which is the minimum arrival time at $d$ for any departure time $t$ at $s$. We present a $(1+ε)$-approximation algorithm for computing $\mathcal{A}(t)$. As part of preprocessing, we execute $O({1 \over ε} \log({\mathcal{V}_{r} \over \mathcal{V}_{c}}))$ shortest path computations for fixed departure times, where $\mathcal{V}_{r}$ is the maximum speed of the robot and $\mathcal{V}_{c}$ is the minimum growth rate of the discs. For any query departure time $t \geq 0$ from $s$, we can approximate the minimum arrival time at the destination in $O(\log ({1 \over ε}) + \log\log({\mathcal{V}_{r} \over \mathcal{V}_{c}}))$ time, within a factor of $1+ε$ of optimal. Since we treat the shortest path computations as black-box functions, for different settings of growing discs, we can plug-in different shortest path algorithms. Thus, the exact time complexity of our algorithm is determined by the running time of the shortest path computations.

cs.DS↗

arXiv2015

Approximating the Integral Fréchet Distance

A pseudo-polynomial time $(1 + \varepsilon)$-approximation algorithm is presented for computing the integral and average Fréchet distance between two given polygonal curves $T_1$ and $T_2$. In particular, the running time is upper-bounded by $\mathcal{O}( ζ^{4}n^4/\varepsilon^{2})$ where $n$ is the complexity of $T_1$ and $T_2$ and $ζ$ is the maximal ratio of the lengths of any pair of segments from $T_1$ and $T_2$. The Fréchet distance captures the minimal cost of a continuous deformation of $T_1$ into $T_2$ and vice versa and defines the cost of a deformation as the maximal distance between two points that are related. The integral Fréchet distance defines the cost of a deformation as the integral of the distances between points that are related. The average Fréchet distance is defined as the integral Fréchet distance divided by the lengths of $T_1$ and $T_2$. Furthermore, we give relations between weighted shortest paths inside a single parameter cell $C$ and the monotone free space axis of $C$. As a result we present a simple construction of weighted shortest paths inside a parameter cell. Additionally, such a shortest path provides an optimal solution for the partial Fréchet similarity of segments for all leash lengths. These two aspects are related to each other and are of independent interest.

cs.CG↗

arXiv2013

Similarity of Polygonal Curves in the Presence of Outliers

The Fréchet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently occurring phenomenon in practice, a robust variant of Fréchet distance is required which absorbs outliers. We study such a variant here. In this modified variant, our objective is to minimize the length of subcurves of two polygonal curves that need to be ignored (MinEx problem), or alternately, maximize the length of subcurves that are preserved (MaxIn problem), to achieve a given Fréchet distance. An exact solution to one problem would imply an exact solution to the other problem. However, we show that these problems are not solvable by radicals over $\mathbb{Q}$ and that the degree of the polynomial equations involved is unbounded in general. This motivates the search for approximate solutions. We present an algorithm, which approximates, for a given input parameter $δ$, optimal solutions for the \MinEx\ and \MaxIn\ problems up to an additive approximation error $δ$ times the length of the input curves. The resulting running time is upper bounded by $\mathcal{O} \left(\frac{n^3}δ \log \left(\frac{n}δ \right)\right)$, where $n$ is the complexity of the input polygonal curves.

cs.CG↗

arXiv2012

Visiting All Sites with Your Dog

Given a polygonal curve P, a pointset S, and an ε> 0, we study the problem of finding a polygonal curve Q whose vertices are from S and has a Frechet distance less or equal to εto curve P. In this problem, Q must visit every point in S and we are allowed to reuse points of pointset in building Q. First, we show that this problem in NP-Complete. Then, we present a polynomial time algorithm for a special cases of this problem, when P is a convex polygon.

cs.CG↗