We revisit the k-SECLUDED TREE problem. Given a vertex-weighted undirected graph G, its objective is to find a maximum-weight induced subtree T whose open neighborhood has size at most k. We present a fixed-parameter ...
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We revisit the k-SECLUDED TREE problem. Given a vertex-weighted undirected graph G, its objective is to find a maximum-weight induced subtree T whose open neighborhood has size at most k. We present a fixed-parameter tractable algorithm that solves the problem in time 2O(k log k) & BULL;nO(1), improving on a double-exponential running time from earlier work by Golovach, Heggernes, Lima, and Montealegre. Starting from a single vertex, our algorithm grows a k-secluded tree by branching on vertices in the open neighborhood of the current tree T. To bound the branching depth, we prove a structural result that can be used to identify a vertex that belongs to the neighborhood of any k-secluded supertree T' T once the open neighborhood of T becomes sufficiently large. We extend the algorithm to enumerate compact descriptions of all maximum-weight k-secluded trees, which allows us to count them as well.& COPY;2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
We propose an optimal design model for determining light sources, powers, layout modes, and equipment spacing of lamps in tunnels that not only effectively reduce the overall installation & operation cost and bus ...
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We propose an optimal design model for determining light sources, powers, layout modes, and equipment spacing of lamps in tunnels that not only effectively reduce the overall installation & operation cost and bus also ease the complexity of manual calculations during the design process of tunnel lighting systems. Firstly, the optimal objective functions considering the construction & installation and energy consumption cost are given in the design of tunnel lighting systems;secondly, the design constraints of tunnel lighting systems are analyzed, which include the demand and design brightness, the minimum and maximum equipment spacings and so on. Then, in order to compare the differences between different optimal design parameters, an enumeration algorithm is proposed. Finally, the YanPengShan tunnel in Leshan City, Zhejiang province, is taken as an example to analyze the influence of different design parameters of tunnel lighting systems on the overall cost of the system under various conditions.
In the context of community detection, correlation clustering (CC) provides a measure of balance for social networks as well as a tool to explore their structures. However, CC does not encompass features such as the m...
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In the context of community detection, correlation clustering (CC) provides a measure of balance for social networks as well as a tool to explore their structures. However, CC does not encompass features such as the mediation between the clusters, which could be all the more relevant with the recent rise of ideological polarization. In this work, we study correlation clustering under mediation (CCM), a new variant of CC in which a set of mediators is determined. This new signed graph clustering problem is proved to be NP-hard and formulated as an integer programming formulation. An extensive investigation of the mediation set structure leads to the development of two efficient exact enumeration algorithms for CCM. The first one exhaustively enumerates the maximal sets of mediators in order to provide several relevant solutions. The second algorithm implements a pruning mechanism, which drastically reduces the size of the exploration tree in order to return a single optimal solution. Computational experiments are presented on two sets of instances: signed networks representing voting activity in the European Parliament and random signed graphs.
Background: The main challenge in de novo genome assembly of DNA-seq data is certainly to deal with repeats that are longer than the reads. In de novo transcriptome assembly of RNA-seq reads, on the other hand, this p...
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Background: The main challenge in de novo genome assembly of DNA-seq data is certainly to deal with repeats that are longer than the reads. In de novo transcriptome assembly of RNA-seq reads, on the other hand, this problem has been underestimated so far. Even though we have fewer and shorter repeated sequences in transcriptomics, they do create ambiguities and confuse assemblers if not addressed properly. Most transcriptome assemblers of short reads are based on de Bruijn graphs (DBG) and have no clear and explicit model for repeats in RNA-seq data, relying instead on heuristics to deal with them. Results: The results of this work are threefold. First, we introduce a formal model for representing high copy-number and low-divergence repeats in RNA-seq data and exploit its properties to infer a combinatorial characteristic of repeat-associated subgraphs. We show that the problem of identifying such subgraphs in a DBG is NP-complete. Second, we show that in the specific case of local assembly of alternative splicing (AS) events, we can implicitly avoid such subgraphs, and we present an efficient algorithm to enumerate AS events that are not included in repeats. Using simulated data, we show that this strategy is significantly more sensitive and precise than the previous version of KisSplice (Sacomoto et al. in WABI, pp 99-111, 1), Trinity (Grabherr et al. in Nat Biotechnol 29(7): 644-652, 2), and Oases (Schulz et al. in Bioinformatics 28(8): 1086-1092, 3), for the specific task of calling AS events. Third, we turn our focus to full-length transcriptome assembly, and we show that exploring the topology of DBGs can improve de novo transcriptome evaluation methods. Based on the observation that repeats create complicated regions in a DBG, and when assemblers try to traverse these regions, they can infer erroneous transcripts, we propose a measure to flag transcripts traversing such troublesome regions, thereby giving a confidence level for each transcript. The originalit
Background: Phylogenetic tree reconciliation is the approach of choice for investigating the coevolution of sets of organisms such as hosts and parasites. It consists in a mapping between the parasite tree and the hos...
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Background: Phylogenetic tree reconciliation is the approach of choice for investigating the coevolution of sets of organisms such as hosts and parasites. It consists in a mapping between the parasite tree and the host tree using event-based maximum parsimony. Given a cost model for the events, many optimal reconciliations are however possible. Any further biological interpretation of them must therefore take this into account, making the capacity to enumerate all optimal solutions a crucial point. Only two algorithms currently exist that attempt such enumeration;in one case not all possible solutions are produced while in the other not all cost vectors are currently handled. The objective of this paper is two-fold. The first is to fill this gap, and the second is to test whether the number of solutions generally observed can be an issue in terms of interpretation. Results: We present a polynomial-delay algorithm for enumerating all optimal reconciliations. We show that in general many solutions exist. We give an example where, for two pairs of host-parasite trees having each less than 41 leaves, the number of solutions is 5120, even when only time-feasible ones are kept. To facilitate their interpretation, those solutions are also classified in terms of how many of each event they contain. The number of different classes of solutions may thus be notably smaller than the number of solutions, yet they may remain high enough, in particular for the cases where losses have cost 0. In fact, depending on the cost vector, both numbers of solutions and of classes thereof may increase considerably. To further deal with this problem, we introduce and analyse a restricted version where host switches are allowed to happen only between species that are within some fixed distance along the host tree. This restriction allows us to reduce the number of time-feasible solutions while preserving the same optimal cost, as well as to find time-feasible solutions with a cost close to the
In sneak circuit analysis,it demands to identify the basic topological patterns which are the causes of sneak circuits. In this paper we formulate the problem of identifying the basic topological patterns into that of...
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In sneak circuit analysis,it demands to identify the basic topological patterns which are the causes of sneak circuits. In this paper we formulate the problem of identifying the basic topological patterns into that of enumerating subgraphs homeomorphic to five specific signed trees in signed graphs,and give methods to simplify signed graphs and an algorithm to find all paths from a given vertex to a set of vertices of degree one in a *** propose a sketch algorithm for enumerating subgraphs homeomorphic to the specific signed trees and present an example of topological patterns identification using our methods.
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