Friedrich, Tobias; Krejca, Martin S.; Lagodzinski, J. A. Gregor; Rizzo, Manuel; Zahn, Arthur Memetic Genetic Algorithms for Time Series Compression by Piecewise Linear ApproximationInternational Conference on Neural Information Processing (ICONIP) 2020: 592–604
Time series are sequences of data indexed by time. Such data are collected in various domains, often in massive amounts, such that storing them proves challenging. Thus, time series are commonly stored in a compressed format. An important compression approach is piecewise linear approximation (PLA), which only keeps a small set of time points and interpolates the remainder linearly. Picking a subset of time points such that the PLA minimizes the mean squared error to the original time series is a challenging task, naturally lending itself to heuristics. We propose the piecewise linear approximation genetic algorithm (PLA-GA) for compressing time series by PLA. The PLA-GA is a memetic \((\mu + \lambda)\) GA that makes use of two distinct operators tailored to time series compression. First, we add special individuals to the initial population that are derived using established PLA heuristics. Second, we propose a novel local search operator that greedily improves a compressed time series. We compare the PLA-GA empirically with existing evolutionary approaches and with a deterministic PLA algorithm, known as Bellman's algorithm, that is optimal for the restricted setting of sampling. In both cases, the PLA-GA approximates the original time series better and quicker. Further, it drastically outperforms Bellman's algorithm with increasing instance size with respect to run time until finding a solution of equal or better quality -- we observe speed-up factors between 7 and 100 for instances of 90,000 to 100,000 data points.
Feldmann, Andreas; Issac, Davis; Rai, Ashutosh Fixed-Parameter Tractability of the Weighted Edge Clique Partition ProblemInternational Symposium on Parameterized and Exact Computation (IPEC) 2020: 1–16
We develop an FPT algorithm and a bi-kernel for the Weighted Edge Clique Partition (WECP) problem, where a graph with \(n\) vertices and integer edge weights is given together with an integer \(k\), and the aim is to find \(k\) cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into \(k\) cliques. It was shown that ECP admits a kernel with \(k^2\) vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of \( 2^{O(k^2)}\) \(n^{O(1)}\) [Issac, 2019]. For WECP we develop a bi-kernel with \(4^k\) vertices, and an algorithm with runtime \(2^{O(k^{3/2}w^{1/2}\log(k/w))} n^{O(1)}\), where \(w\) is the maximum edge weight. The latter in particular improves the runtime for ECP to \(2^{O(k^{3/2}\log k)} n^{O(1)}\).
Bilò, Davide; Friedrich, Tobias; Lenzner, Pascal; Melnichenko, Anna; Molitor, Louise Fair Tree Connection Games with Topology-Dependent Edge CostFoundations of Software Technology and Theoretical Computer Science (FSTTCS) 2020: 15:1–15:15
How do rational agents self-organize when trying to connect to a common target? We study this question with a simple tree formation game which is related to the well-known fair single-source connection game by Anshelevich et al.(FOCS'04) and selfish spanning tree games by Gourvès and Monnot (WINE'08). In our game agents correspond to nodes in a network that activate a single outgoing edge to connect to the common target node (possibly via other nodes). Agents pay for their path to the common target, and edge costs are shared fairly among all agents using an edge. The main novelty of our model is dynamic edge costs that depend on the in-degree of the respective endpoint. This reflects that connecting to popular nodes that have increased internal coordination costs is more expensive since they can charge higher prices for their routing service. In contrast to related models, we show that equilibria are not guaranteed to exist, but we prove the existence for infinitely many numbers of agents. Moreover, we analyze the structure of equilibrium trees and employ these insights to prove a constant upper bound on the Price of Anarchy as well as non-trivial lower bounds on both the Price of Anarchy and the Price of Stability. We also show that in comparison with the social optimum tree the overall cost of an equilibrium tree is more fairly shared among the agents. Thus, we prove that self-organization of rational agents yields on average only slightly higher cost per agent compared to the centralized optimum, and at the same time, it induces a more fair cost distribution. Moreover, equilibrium trees achieve a beneficial trade-off between a low height and low maximum degree, and hence these trees might be of independent interest from a combinatorics point-of-view. We conclude with a discussion of promising extensions of our model.