Restless Temporal Path Parameterized Above Lower Bounds

Reachability questions are one of the most fundamental algorithmic primitives in temporal graphs - graphs whose edge set changes over discrete time steps. A core problem here is the NP-hard Short Restless Temporal Path: given a temporal graph G, two distinct vertices s and z, and two numbers ? and k, is there a ?-restless temporal s-z path of length at most k? A temporal path is a path whose edges appear in chronological order and a temporal path is ?-restless if two consecutive path edges appear at most ? time steps apart from each other. Among others, this problem has applications in neuroscience and epidemiology. While Short Restless Temporal Path is known to be computationally hard, e.g., it is NP-hard even if the temporal graph consists of three discrete time steps and it is W[1]-hard when parameterized by the feedback vertex number of the underlying graph, it is fixed-parameter tractable when parameterized by the path length k. We improve on this by showing that Short Restless Temporal Path can be solved in (randomized) 4^(k-d)|G|^O(1) time, where d is the minimum length of a temporal s-z path

Parameterized Algorithms for Diverse Multistage Problems

The world is rarely static - many problems need not only be solved once but repeatedly, under changing conditions. This setting is addressed by the multistage view on computational problems. We study the diverse multistage variant, where consecutive solutions of large variety are preferable to similar ones, e.g. for reasons of fairness or wear minimization. While some aspects of this model have been tackled before, we introduce a framework allowing us to prove that a number of diverse multistage problems are fixed-parameter tractable by diversity, namely Perfect Matching, s-t Path, Matroid Independent Set, and Plurality Voting. This is achieved by first solving special, colored variants of these problems, which might also be of independent interest

The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing

The Parameterized Algorithms and Computational Experiments challenge (PACE) 2021 was devoted to engineer algorithms solving the NP-hard Cluster Editing problem, also known as Correlation Clustering: Given an undirected graph the task is to compute a minimum number of edges to insert or remove in a way that the resulting graph is a cluster graph, that is, a graph in which each connected component is a clique. Altogether 67 participants from 21 teams, 11 countries, and 3 continents submitted their implementations to the competition. In this report, we describe the setup of the challenge, the selection of benchmark instances, and the ranking of the participating teams. We also briefly discuss the approaches used in the submitted solvers

Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments

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 O~(m sqrt{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) linear-time data reduction rules for the positive-integer-weighted case. Moreover, we experimentally demonstrate that these data reduction rules provide significant speedups of the state-of-the art implementation for computing matchings in real-world graphs: the average speedup is 3800% in the unweighted case and "just" 30% in the weighted case

The enzyme mechanism of a de novo designed and evolved aldolase

The combination of computational enzyme design and laboratory evolution is a successful strategy for the development of biocatalysts with non-natural function, one example being the artificial retroaldolase RA95.1,2 This enzyme utilizes amine catalysis via a reactive lysine residue to cleave the unnatural aldol substrate methodol (Figure 1A). The low initial catalytic activity of the computational design was improved tremendously over many rounds of directed evolution, yielding an efficient biocatalyst for both aldol cleavage as well as synthesis with rate acceleration and stereoselectivity comparable to natural aldolases (Figure 1B).3,4 Key to this success was an ultrahigh-throughput (uHTP) screening technique applied for the late stages of optimization.4 In this work, we analyzed changes in enzyme mechanism along the evolutionary trajectory of RA95 that led to more efficient catalysis. To that end, we determined the rate-limiting step for different enzyme variants by probing individual steps of the aldolase mechanism kinetically. We found a shift towards product release being overall rate-limiting for aldol cleavage catalyzed by highly evolved variants of RA95. Specifically, the conversion between Schiff base and enamine intermediate formed from acetone, a (de-)protonation-dependent process, is the slowest step we probed. Our results indicate that uHTP screening is essential to efficiently evolve a multi-step enzyme mechanism, as it allows the optimization of several mechanistic steps in parallel. By comparing our findings to kinetic and structural studies on natural aldolases, we provide valuable feedback to improve future laboratory evolution approaches as well as the success rate of computational enzyme design. Please click Additional Files below to see the full abstract