Adversarial patrolling with spatially uncertain alarm signals

When securing complex infrastructures or large environments, constant surveillance of every area is not affordable. To cope with this issue, a common countermeasure is the usage of cheap but wide-ranged sensors, able to detect suspicious events that occur in large areas, supporting patrollers to improve the effectiveness of their strategies. However, such sensors are commonly affected by uncertainty. In the present paper, we focus on spatially uncertain alarm signals. That is, the alarm system is able to detect an attack but it is uncertain on the exact position where the attack is taking place. This is common when the area to be secured is wide, such as in border patrolling and fair site surveillance. We propose, to the best of our knowledge, the first Patrolling Security Game where a Defender is supported by a spatially uncertain alarm system, which non-deterministically generates signals once a target is under attack. We show that finding the optimal strategy is FNP-hard even in tree graphs and APX-hard in arbitrary graphs. We provide two (exponential time) exact algorithms and two (polynomial time) approximation algorithms. Finally, we show that, without false positives and missed detections, the best patrolling strategy reduces to stay in a place, wait for a signal, and respond to it at best. This strategy is optimal even with non-negligible missed detection rates, which, unfortunately, affect every commercial alarm system. We evaluate our methods in simulation, assessing both quantitative and qualitative aspects

Combinatorial Optimization

Combinatorial Optimization is an active research area that developed from the rich interaction among many mathematical areas, including combinatorics, graph theory, geometry, optimization, probability, theoretical computer science, and many others. It combines algorithmic and complexity analysis with a mature mathematical foundation and it yields both basic research and applications in manifold areas such as, for example, communications, economics, traffic, network design, VLSI, scheduling, production, computational biology, to name just a few. Through strong inner ties to other mathematical fields it has been contributing to and benefiting from areas such as, for example, discrete and convex geometry, convex and nonlinear optimization, algebraic and topological methods, geometry of numbers, matroids and combinatorics, and mathematical programming. Moreover, with respect to applications and algorithmic complexity, Combinatorial Optimization is an essential link between mathematics, computer science and modern applications in data science, economics, and industry

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Shortest Distances as Enumeration Problem

We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$ are vertices with shortest distance $d(u, v)$ -- are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs $(u, v, \infty)$, or excluding the self-distances $(u, u, 0)$) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.Comment: Updated version adds the study of space complexit

A hybrid algorithm for Bayesian network structure learning with application to multi-label learning

We present a novel hybrid algorithm for Bayesian network structure learning, called H2PC. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. The algorithm is based on divide-and-conquer constraint-based subroutines to learn the local structure around a target variable. We conduct two series of experimental comparisons of H2PC against Max-Min Hill-Climbing (MMHC), which is currently the most powerful state-of-the-art algorithm for Bayesian network structure learning. First, we use eight well-known Bayesian network benchmarks with various data sizes to assess the quality of the learned structure returned by the algorithms. Our extensive experiments show that H2PC outperforms MMHC in terms of goodness of fit to new data and quality of the network structure with respect to the true dependence structure of the data. Second, we investigate H2PC's ability to solve the multi-label learning problem. We provide theoretical results to characterize and identify graphically the so-called minimal label powersets that appear as irreducible factors in the joint distribution under the faithfulness condition. The multi-label learning problem is then decomposed into a series of multi-class classification problems, where each multi-class variable encodes a label powerset. H2PC is shown to compare favorably to MMHC in terms of global classification accuracy over ten multi-label data sets covering different application domains. Overall, our experiments support the conclusions that local structural learning with H2PC in the form of local neighborhood induction is a theoretically well-motivated and empirically effective learning framework that is well suited to multi-label learning. The source code (in R) of H2PC as well as all data sets used for the empirical tests are publicly available.Comment: arXiv admin note: text overlap with arXiv:1101.5184 by other author