Search Results (12)

Perfect Roman Dominating Functions and Unique Response Roman Dominating Functions are two ways to translate perfect code into the framework of Roman Dominating Functions. We also consider the enumeration of minimal Perfect Roman Dominating Functions and show a tight relation to minimal Roman Dominating Functions. Furthermore, we consider the complexity of the underlying decision problems Perfect Roman Domination and Unique Response Roman Domination on special graph classes. For instance, split graphs are the first graph class for which Unique Response Roman Domination is polynomial-time solvable, while Perfect Roman Domination is NP-complete. Beyond this, we give polynomial-time algorithms for Perfect Roman Domination on interval graphs and for both decision problems on cobipartite graphs. However, both problems are NP-complete on chordal bipartite graphs. We show that both problems are $\mathsf{W}\left[1\right]$-complete if parameterized by solution size and FPT if parameterized by the dual parameter or by clique width. Full article

In the directed co-graph edge-deletion problem, we are given a directed graph and an integer k, and the question is whether we can delete, at most, k edges so that the resulting graph is a directed co-graph. In this paper, we make two minor contributions. Firstly, we show that the problem is NP-hard. Then, we show that directed co-graphs are fully characterized by eight forbidden structures, each having, at most, six edges. Based on the symmetry properties and several refined observations, we develop a branching algorithm with a running time of $O\left({2.733}^k\right)$, which is significantly more efficient compared to the brute-force algorithm, which has a running time of $O\left(6^k\right)$. Full article

Recently, the estimation of remaining useful life (RUL) for two-phase nonlinear degrading devices has shown rising momentum for ensuring their safe and reliable operation. The degradation processes of such systems are influenced by the temporal variability, unit-to-unit variability, and measurement variability jointly. However, current studies only consider these three sources of variability partially. To this end, this paper presents a two-phase nonlinear degradation model with three-source variability based on the nonlinear Wiener process. Then, the approximate analytical solution of the RUL with three-source variability is derived under the concept of the first passage time (FPT). For better implementation, the offline model parameter estimation is conducted by the maximum likelihood estimation (MLE), and the Bayesian rule in conjunction with the Kalman filtering (KF) algorithm are utilized for the online model updating. Finally, the effectiveness of the proposed approach is validated through a numerical example and a practical case study of the capacitor degradation data. The results show that it is necessary to incorporate three-source variability simultaneously into the RUL prediction of the two-phase nonlinear degrading systems. Full article

Aiming at the common problems, such as noise pollution, low contrast, and color distortion in underwater images, and the characteristics of holothurian recognition, such as morphological ambiguity, high similarity with the background, and coexistence of special ecological scenes, this paper proposes an underwater holothurian target-detection algorithm (FA-CenterNet), based on improved CenterNet and scene feature fusion. First, to reduce the model’s occupancy of embedded device resources, we use EfficientNet-B3 as the backbone network to reduce the model’s Params and FLOPs. At the same time, EfficientNet-B3 increases the depth and width of the model, which improves the accuracy of the model. Then, we design an effective FPT (feature pyramid transformer) combination module to fully focus and mine the information on holothurian ecological scenarios of different scales and spaces (e.g., holothurian spines, reefs, and waterweeds are often present in the same scenario as holothurians). The co-existing scene information can be used as auxiliary features to detect holothurians, which can improve the detection ability of fuzzy and small-sized holothurians. Finally, we add the AFF module to realize the deep fusion of the shallow-detail and high-level semantic features of holothurians. The results show that the method presented in this paper yields better results on the 2020 CURPC underwater target-detection image dataset with an AP50 of 83.43%, Params of 15.90 M, and FLOPs of 25.12 G compared to other methods. In the underwater holothurian-detection task, this method improves the accuracy of detecting holothurians with fuzzy features, a small size, and dense scene. It also achieves a good balance between detection accuracy, Params, and FLOPs, and is suitable for underwater holothurian detection in most situations. Full article

The partial transmit sequence (PTS) technique is a fairly suitable scheme to mitigate the high peak-to-average power ratio (PAPR) problem inherent in 5G multicarrier systems, especially considering a high-order QAM modulation design. However, the high computational complexity level and the speed of the convergence for optimizing the phases of the transmitting signal restrict this technique in practical applications. In this paper, a low-complexity frequency-domain-evaluated PTS (F-PTS) based on a spacing multiobjective (SMO) processing algorithm is proposed to reduce the PAPR values. The PAPR performance are accurately predicted in terms of modifying relative dispersion in the frequency domain. As a result, the complexity of searching the optimal phase factors and IFFT computing is simplified. Moreover, a frequency-domain- and time-domain-evaluating PTS (FTD-PTS) is employed to search the optimal solution with a reasonable complexity. Simulation results verify that the operation rate of F-PTS is significantly improved after transferring the exhaustive search strategy of PTS into the SMO algorithm, and the F-PTS PAPR reduction performance is just 0.3 dB away from theoretical optimal performance. The FTD-PTS spends an acceptable operation rate to obtain optimal PAPR reduction performance, which subtracts 0.5 and 0.6 dB more than PSO-PTS and conventional PTS at $CCDF={10}^{-3}$, respectively. Full article

Color coding is an algorithmic technique used in parameterized complexity theory to detect “small” structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color pattern. We transfer color coding to the world of descriptive complexity theory by characterizing—purely in terms of the syntactic structure of describing formulas—when the powerful second-order quantifiers representing a random coloring can be replaced by equivalent, simple first-order formulas. Building on this result, we identify syntactic properties of first-order quantifiers that can be eliminated from formulas describing parameterized problems. The result applies to many packing and embedding problems, but also to the long path problem. Together with a new result on the parameterized complexity of formula families involving only a fixed number of variables, we get that many problems lie in FPT just because of the way they are commonly described using logical formulas. Full article

We present a detailed survey of results and two new results on graphical models of uncertainty and associated optimization problems. We focus on two well-studied models, namely, the Random Failure (RF) model and the Linear Reliability Ordering (LRO) model. We present an FPT algorithm parameterized by the product of treewidth and max-degree for maximizing expected coverage in an uncertain graph under the RF model. We then consider the problem of finding the maximal core in a graph, which is known to be polynomial time solvable. We show that the Probabilistic-Core problem is polynomial time solvable in uncertain graphs under the LRO model. On the other hand, under the RF model, we show that the Probabilistic-Core problem is W[1]-hard for the parameter d, where d is the minimum degree of the core. We then design an FPT algorithm for the parameter treewidth. Full article

In this work, we study the d-Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of r solutions of size at most k each, which has recently been introduced to the field of parameterized complexity. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process that models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are fixed-parameter tractable in $k+r$ for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of ‘base’ solutions, computes a maximally diverse collection of solutions. We believe that this could be of independent interest. Full article

Chen and Flum showed that any FPT-approximation of the k-Clique problem is not in para- ${\mathsf{AC}}^{\mathsf{0}}$ and the k-DominatingSet (k-DomSet) problem could not be computed by para- ${\mathsf{AC}}^{\mathsf{0}}$ circuits. It is natural to ask whether the $f(k)$ -approximation of the k-DomSet problem is in para- ${\mathsf{AC}}^{\mathsf{0}}$ for some computable function f. Very recently it was proved that assuming $\mathsf{W}[\mathsf{1}]\ne \mathsf{FPT}$ , the k-DomSet problem cannot be $f(k)$ -approximated by FPT algorithms for any computable function f by S., Laekhanukit and Manurangsi and Lin, seperately. We observe that the constructions used in Lin’s work can be carried out using constant-depth circuits, and thus we prove that para- ${\mathsf{AC}}^{\mathsf{0}}$ circuits could not approximate this problem with ratio $f(k)$ for any computable function f. Moreover, under the hypothesis that the 3-CNF-SAT problem cannot be computed by constant-depth circuits of size $2^{\epsilon n}$ for some $\epsilon >0$ , we show that constant-depth circuits of size $n^{o(k)}$ cannot distinguish graphs whose dominating numbers are either ≤k or > ${\left(\frac{logn}{3loglogn}\right)}^{1/k}$ . However, we find that the hypothesis may be hard to settle by showing that it implies $\mathsf{NP}⊈{\mathsf{NC}}^{\mathsf{1}}$ . Full article

Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay in the context of general modification problems. We study these problems considering two different orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility and is used in the context of lexicographic order. The second one shows that the existence of a neighbourhood structure among the solutions implies the existence of an algorithm running with FPT delay which outputs all solutions ordered non-decreasingly by their size. Full article

We introduce and study the computational power of Oritatami, a theoretical model that explores greedy molecular folding, whereby a molecular strand begins to fold before its production is complete. This model is inspired by our recent experimental work demonstrating the construction of shapes at the nanoscale from RNA, where strands of RNA fold into programmable shapes during their transcription from an engineered sequence of synthetic DNA. In the model of Oritatami, we explore the process of folding a single-strand bit by bit in such a way that the final fold emerges as a space-time diagram of computation. One major requirement in order to compute within this model is the ability to program a single sequence to fold into different shapes dependent on the state of the surrounding inputs. Another challenge is to embed all of the computing components within a contiguous strand, and in such a way that different fold patterns of the same strand perform different functions of computation. Here, we introduce general design techniques to solve these challenges in the Oritatami model. Our main result in this direction is the demonstration of a periodic Oritatami system that folds upon itself algorithmically into a prescribed set of shapes, depending on its current local environment, and whose final folding displays the sequence of binary integers from 0 to $N=2^k-1$ with a seed of size $O\left(k\right)$ . We prove that designing Oritatami is NP-hard in the number of possible local environments for the folding. Nevertheless, we provide an efficient algorithm, linear in the length of the sequence, that solves the Oritatami design problem when the number of local environments is a small fixed constant. This shows that this problem is in fact fixed parameter tractable (FPT) and can thus be solved in practice efficiently. We hope that the numerous structural strategies employed in Oritatami enabling computation will inspire new architectures for computing in RNA that take advantage of the rapid kinetic-folding of RNA. Full article

Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime’s closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration. Full article