The electric vehicle sharing problem (EVSP) arises from the planning and operation of one-way electric car-sharing systems. It aims to maximize the total rental time of a fleet of electric vehicles while ensuring that all the demands of the customer are fulfilled. In this paper, we expand the knowledge on the complexity of the EVSP by showing that it is NP-hard to approximate it to within a factor of $n^{1-\epsilon}$ in polynomial time, for any $\epsilon > 0$, where $n$ denotes the number of customers, unless P = NP. In addition, we also show that the problem does not have a monotone structure, which can be detrimental to the development of heuristics employing constructive strategies. Moreover, we propose a novel approach for the modeling of the EVSP based on energy flows in the network. Based on the new model, we propose a relax-and-fix strategy and an exact algorithm that uses a warm-start solution obtained from our heuristic approach. We report computational results comparing our formulation with the best-performing formulation in the literature. The results show that our formulation outperforms the previous one concerning the number of optimal solutions obtained, optimality gaps, and computational times. Previously, $32.7\%$ of the instances remained unsolved (within a time limit of one hour) by the best-performing formulation in the literature, while our formulation obtained optimal solutions for all instances. To stress our approaches, two more challenging new sets of instances were generated, for which we were able to solve $49.5\%$ of the instances, with an average optimality gap of $2.91\%$ for those not solved optimally.
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Fast moving unmanned aerial vehicles (UAVs) are well suited for aerial surveillance, but are limited by their battery capacity. To increase their endurance UAVs can be refueled on slow moving unmanned ground vehicles (UGVs). The cooperative routing of UAV-UGV multi-agent system to survey vast regions within their speed and fuel constraints is a computationally challenging problem, but can be simplified with heuristics. Here we present multiple heuristics to enable feasible and sufficiently optimal solutions to the problem. Using the UAV fuel limits and the minimum set cover algorithm, the UGV refueling stops are determined. These refueling stops enable the allocation of mission points to the UAV and UGV. A standard traveling salesman formulation and a vehicle routing formulation with time windows, dropped visits, and capacity constraints is used to solve for the UGV and UAV route, respectively. Experimental validation on a small-scale testbed (//tiny.cc/8or8vz) underscores the effectiveness of our multi-agent approach.
Cook and Reckhow 1979 pointed out that NP is not closed under complementation iff there is no propositional proof system that admits polynomial size proofs of all tautologies. Theory of proof complexity generators aims at constructing sets of tautologies hard for strong and possibly for all proof systems. We focus at a conjecture from K.2004 in foundations of the theory that there is a proof complexity generator hard for all proof systems. This can be equivalently formulated (for p-time generators) without a reference to proof complexity notions as follows: * There exist a p-time function $g$ stretching each input by one bit such that its range intersects all infinite NP sets. We consider several facets of this conjecture, including its links to bounded arithmetic (witnessing and independence results), to time-bounded Kolmogorov complexity, to feasible disjunction property of propositional proof systems and to complexity of proof search. We argue that a specific gadget generator from K.2009 is a good candidate for $g$. We define a new hardness property of generators, the $\bigvee$-hardness, and shows that one specific gadget generator is the $\bigvee$-hardest (w.r.t. any sufficiently strong proof system). We define the class of feasibly infinite NP sets and show, assuming a hypothesis from circuit complexity, that the conjecture holds for all feasibly infinite NP sets.
In this paper, we present a method to encrypt dynamic controllers that can be implemented through most homomorphic encryption schemes, including somewhat, leveled fully, and fully homomorphic encryption. To this end, we represent the output of the given controller as a linear combination of a fixed number of previous inputs and outputs. As a result, the encrypted controller involves only a limited number of homomorphic multiplications on every encrypted data, assuming that the output is re-encrypted and transmitted back from the actuator. A guidance for parameter choice is also provided, ensuring that the encrypted controller achieves predefined performance for an infinite time horizon. Furthermore, we propose a customization of the method for Ring-Learning With Errors (Ring-LWE) based cryptosystems, where a vector of messages can be encrypted into a single ciphertext and operated simultaneously, thus reducing computation and communication loads. Unlike previous results, the proposed customization does not require extra algorithms such as rotation, other than basic addition and multiplication. Simulation results demonstrate the effectiveness of the proposed method.
Shared Mobility Services (SMS), e.g., Demand-Responsive Transit (DRT) or ride-sharing, can improve mobility in low-density areas, often poorly served by conventional Public Transport (PT). Such improvement is mostly quantified via basic performance indicators, like wait or travel time. However, accessibility indicators, measuring the ease of reaching surrounding opportunities (e.g., jobs, schools, shops, ...), would be a more comprehensive indicator. To date, no method exists to quantify the accessibility of SMS based on empirical measurements. Indeed, accessibility is generally computed on graph representations of PT networks, but SMS are dynamic and do not follow a predefined network. We propose a spatial-temporal statistical method that takes as input observed trips of a SMS acting as a feeder for PT and summarized such trips in a graph. On such a graph, we compute classic accessibility indicators. We apply our method to a MATSim simulation study concerning DRT in Paris-Saclay.
Over the course of the past two decades, a substantial body of research has substantiated the viability of utilising cardiac signals as a biometric modality. This paper presents a novel approach for patient identification in healthcare systems using electrocardiogram signals. A convolutional neural network is used to classify users based on images extracted from ECG signals. The proposed identification system is evaluated in multiple databases, providing a comprehensive understanding of its potential in real-world scenarios. The impact of Cardiovascular Diseases on generic user identification has been largely overlooked in previous studies. The presented method takes into account the cardiovascular condition of the patients, ensuring that the results obtained are not biased or limited. Furthermore, the results obtained are consistent and reliable, with lower error rates and higher accuracy metrics, as demonstrated through extensive experimentation. All these features make the proposed method a valuable contribution to the field of patient identification in healthcare systems, and make it a strong contender for practical applications.
This paper considers an uplink Internet of Things system with synchronous periodic traffic, where multiple devices generate their status updates at the beginning of each global frame and attempt to send them to a common access point. To achieve a low network-wide age of information (AoI) in an easily implementable manner, we require each device to adopt an age-dependent random access protocol, i.e., to transmit with a certain probability only when its corresponding AoI reaches a certain threshold. We analyze the time-average expected AoI by a multi-layer Markov model where an external infinite-horizon Markov chain manages the jumps between the beginnings of frames, while two internal finite-horizon Markov chains manage the evolution during an arbitrary frame for different cases. Simulation results verify the accuracy of the modeling and the AoI advantage over age-independent schemes.
Interpreting objects with basic geometric primitives has long been studied in computer vision. Among geometric primitives, superquadrics are well known for their ability to represent a wide range of shapes with few parameters. However, as the first and foremost step, recovering superquadrics accurately and robustly from 3D data still remains challenging. The existing methods are subject to local optima and sensitive to noise and outliers in real-world scenarios, resulting in frequent failure in capturing geometric shapes. In this paper, we propose the first probabilistic method to recover superquadrics from point clouds. Our method builds a Gaussian-uniform mixture model (GUM) on the parametric surface of a superquadric, which explicitly models the generation of outliers and noise. The superquadric recovery is formulated as a Maximum Likelihood Estimation (MLE) problem. We propose an algorithm, Expectation, Maximization, and Switching (EMS), to solve this problem, where: (1) outliers are predicted from the posterior perspective; (2) the superquadric parameter is optimized by the trust-region reflective algorithm; and (3) local optima are avoided by globally searching and switching among parameters encoding similar superquadrics. We show that our method can be extended to the multi-superquadrics recovery for complex objects. The proposed method outperforms the state-of-the-art in terms of accuracy, efficiency, and robustness on both synthetic and real-world datasets. The code is at //github.com/bmlklwx/EMS-superquadric_fitting.git.
The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. Such a problem is $\textsf{NP}$-complete even when the input graph is planar and has maximum degree five. In this paper, we first present a $\mathcal{O}^*(1.4423^{n})$-time algorithm for the problem. We also show how to compute a minimum independent cutset (if any) in the same running time. Since the property of having an independent cutset is MSO$_1$-expressible, our main results are concerned with structural parameterizations for the problem considering parameters that are not bounded by a function of the clique-width of the input. We present $\textsf{FPT}$-time algorithms for the problem considering the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to $P_5$-free graphs. We close by introducing the notion of $\alpha$-domination, which allows us to identify more fixed-parameter tractable and polynomial-time solvable cases.
For autonomous driving, traversability analysis is one of the most basic and essential tasks. In this paper, we propose a novel LiDAR-based terrain modeling approach, which could output stable, complete and accurate terrain models and traversability analysis results. As terrain is an inherent property of the environment that does not change with different view angles, our approach adopts a multi-frame information fusion strategy for terrain modeling. Specifically, a normal distributions transform mapping approach is adopted to accurately model the terrain by fusing information from consecutive LiDAR frames. Then the spatial-temporal Bayesian generalized kernel inference and bilateral filtering are utilized to promote the stability and completeness of the results while simultaneously retaining the sharp terrain edges. Based on the terrain modeling results, the traversability of each region is obtained by performing geometric connectivity analysis between neighboring terrain regions. Experimental results show that the proposed method could run in real-time and outperforms state-of-the-art approaches.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.
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