Validation of Automated Chromosome Recovery in the Reconstruction of Ancestral Gene Order

The RACCROCHE pipeline reconstructs ancestral gene orders and chromosomal contents of the ancestral genomes at all internal vertices of a phylogenetic tree. The strategy is to accumulate a very large number of generalized adjacencies, phylogenetically justified for each ancestor, to produce long ancestral contigs through maximum weight matching. It constructs chromosomes by counting the frequencies of ancestral contig co-occurrences on the extant genomes, clustering these for each ancestor and ordering them. The main objective of this paper is to closely simulate the evolutionary process giving rise to the gene content and order of a set of extant genomes (six distantly related monocots), and to assess to what extent an updated version of RACCROCHE can recover the artificial ancestral genome at the root of the phylogenetic tree relating to the simulated genomes.

Data Reduction for Maximum Matching on Real-World Graphs

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For n -vertex and m -edge graphs, the best-known algorithms run in Õ( m √ n ) time. We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) new (near-)linear-time data reduction rules for both the unweighted and the positive-integer-weighted case. Moreover, we experimentally demonstrate that these data reduction rules provide significant speedups of the state-of-the art implementations for computing matchings in real-world graphs: the average speedup factor is 4.7 in the unweighted case and 12.72 in the weighted case.

Online Dynamic B-Matching

This paper initiates the study of online algorithms for the maximum weight b-matching problem, a generalization of maximum weight matching where each node has at most b≥1 adjacent matching edges. The problem is motivated by emerging optical technologies which allow to enhance datacenter networks with reconfigurable matchings, providing direct connectivity between frequently communicating racks. These additional links may improve network performance, by leveraging spatial and temporal structure in the workload. We show that the underlying algorithmic problem features an intriguing connection to online paging (a.k.a. caching), but introduces a novel challenge. Our main contribution is an online algorithm which is O(b)- competitive; we also prove that this is asymptotically optimal. We complement our theoretical results with extensive trace-driven simulations, based on real-world datacenter workloads as well as synthetic traffic traces.

Stabilizing Weighted Graphs

An edge-weighted graph [Formula: see text] is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in network bargaining games and cooperative matching games, because they characterize instances that admit stable outcomes. We give the first polynomial-time algorithm to find a minimum cardinality subset of vertices whose removal from G yields a stable graph, for any weighted graph G. The algorithm is combinatorial and exploits new structural properties of basic fractional matchings, which are of independent interest. In contrast, we show that the problem of finding a minimum cardinality subset of edges whose removal from a weighted graph G yields a stable graph, does not admit any constant-factor approximation algorithm, unless P = NP. In this setting, we develop an O(Δ)-approximation algorithm for the problem, where Δ is the maximum degree of a node in G.

Kmer2SNP: reference-free SNP calling from raw reads based on matching

The development of DNA sequencing technologies provides the opportunity to call heterozygous SNPs for each individual. SNP calling is a fundamental problem of genetic analysis and has many applications, such as gene-disease diagnosis, drug design, and ancestry inference. Reference-based SNP calling approaches generate highly accurate results, but they face serious limitations especially when high-quality reference genomes are not available for many species. Although reference-free approaches have the potential to call SNPs without using the reference genome, they have not been widely applied on large and complex genomes because existing approaches suffer from low recall/precision or high runtime.We develop a reference-free algorithm Kmer2SNP to call SNP directly from raw reads. Kmer2SNP first computes the k-mer frequency distribution from reads and identifies potential heterozygous k-mers which only appear in one haplotype. Kmer2SNP then constructs a graph by choosing these heterozygous k-mers as vertices and connecting edges between pairs of heterozygous k-mers that might correspond to SNPs. Kmer2SNP further assigns a weight to each edge using overlapping information between heterozygous k-mers, computes a maximum weight matching and finally outputs SNPs as edges between k-mer pairs in the matching.We benchmark Kmer2SNP against reference-free methods including hybrid (assembly-based) and assembly-free methods on both simulated and real datasets. Experimental results show that Kmer2SNP achieves better SNP calling quality while being an order of magnitude faster than the state-of-the-art methods. Kmer2SNP shows the potential of calling SNPs only using k-mers from raw reads without assembly. The source code is freely available at https://github.com/yanboANU/Kmer2SNP.

Randomized scheduling algorithm for virtual output queuing switch at the presence of non-uniform traffic

<span>Virtual Output Queuing (VOQ) is a well-known queuing discipline in data switch architecture that eliminates Head Of Line (HOL) blocking issue. In VOQ scheme, for each output port, a separate FIFO is maintained by each input port. Consequently, a scheduling algorithm is required to determine the order of service to virtual queues at each time slot. Maximum Weight Matching (MWM) is a well-known scheduling algorithm that achieves the entire throughput region. Despite of outstanding attainable throughput, high complexity of MWM makes it an impractical algorithm for implementation in high-speed switches. To overcome this challenge, a number of randomized algorithms have been proposed in the literature. But they commonly perform poorly when input traffic does not uniformly select output ports. In this paper, we propose two randomized algorithms that outperform the well-known formerly proposed solutions. We exploit a method to keep a parametric number of heavy edges from the last time matching and mix it by randomly generated matching to produce a new schedule. Simulation results confirm the superior performance of the proposed algorithms.</span>

Predicting Model and Algorithm in RNA Folding Structure Including Pseudoknots

The prediction of RNA structure with pseudoknots is a nondeterministic polynomial-time hard (NP-hard) problem; according to minimum free energy models and computational methods, we investigate the RNA-pseudoknotted structure. Our paper presents an efficient algorithm for predicting RNA structure with pseudoknots, and the algorithm takes O([Formula: see text]) time and O([Formula: see text]) space, the experimental tests in Rfam10.1 and PseudoBase indicate that the algorithm is more effective and precise. The predicting accuracy, the time complexity and space complexity outperform existing algorithms, such as Maximum Weight Matching (MWM) algorithm, PKNOTS algorithm and Inner Limiting Layer (ILM) algorithm, and the algorithm can predict arbitrary pseudoknots. And there exists a [Formula: see text] ([Formula: see text]) polynomial time approximation scheme in searching maximum number of stackings, and we give the proof of the approximation scheme in RNA-pseudoknotted structure. We have improved several types of pseudoknots considered in RNA folding structure, and analyze their possible transitions between types of pseudoknots.