1,103 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Look Before, Before You Leap: Online Vector Load Balancing with Few Reassignments

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    In this paper we study two fully-dynamic multi-dimensional vector load balancing problems with recourse. The adversary presents a stream of n job insertions and deletions, where each job j is a vector in ?^d_{? 0}. In the vector scheduling problem, the algorithm must maintain an assignment of the active jobs to m identical machines to minimize the makespan (maximum load on any dimension on any machine). In the vector bin packing problem, the algorithm must maintain an assignment of active jobs into a number of bins of unit capacity in all dimensions, to minimize the number of bins currently used. In both problems, the goal is to maintain solutions that are competitive against the optimal solution for the active set of jobs, at every time instant. The algorithm is allowed to change the assignment from time to time, with the secondary objective of minimizing the amortized recourse, which is the average cardinality of the change of the assignment per update to the instance. For the vector scheduling problem, we present two simple algorithms. The first is a randomized algorithm with an O(1) amortized recourse and an O(log d/log log d) competitive ratio against oblivious adversaries. The second algorithm is a deterministic algorithm that is competitive against adaptive adversaries but with a slightly higher competitive ratio of O(log d) and a per-job recourse guarantee bounded by O?(log n + log d log OPT). We also prove a sharper instance-dependent recourse guarantee for the deterministic algorithm. For the vector bin packing problem, we make the so-called small jobs assumption that the size of all jobs in all the coordinates is O(1/log d) and present a simple O(1)-competitive algorithm with O(log n) recourse against oblivious adversaries. For both problems, the main challenge is to determine when and how to migrate jobs to maintain competitive solutions. Our central idea is that for each job, we make these decisions based only on the active set of jobs that are "earlier" than this job in some ordering ? of the jobs

    Farming out : a study.

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    Farming is one of severals ways of arranging for a group of individuals to perform work simultaneously. Farming is attractive. It is a simple concept, and yet it allocates work dynamically, balancing the load automatically. This gives rise to potentially great efficiency; yet the range of applications that can be farmed efficiently and which implementation strategies are the most effective has not been classified. This research has investigated the types of application, design and implementation that farm efficiently on computer systems constructed from a network of communicating parallel processors. This research shows that all applications can be farmed and identifies those concerns that dictate efficiency. For the first generation of transputer hardware, extensive experiments have been performed using Occam, independent of any specific application. This study identified the boundary conditions that dictate which design parameters farm efficiently. These boundary conditions are expressed in a general form that is directly amenable to other architectures. The specific quantitative results are of direct use to others who wish to implement farms on this architecture. Because of farming’s simplicity and potential for high efficiency, this work concludes that architects of parallel hardware should consider binding this paradigm into future systems so as to enable the dynamic allocation of processes to processors to take place automatically. As well as resulting in high levels of machine utilisation for all programs, this would also permanently remove the burden of allocation from the programmer

    Algorithms for sparse convolution and sublinear edit distance

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    In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-sensitive and sublinear-time algorithms for two important problems. (1) Sparse Convolution: Computing the convolution of two vectors is a basic algorithmic primitive with applications across all of Computer Science and Engineering. In the sparse convolution problem we assume that the input and output vectors have at most t nonzero entries, and the goal is to design algorithms with running times dependent on t. For the special case where all entries are nonnegative, which is particularly important for algorithm design, it is known since twenty years that sparse convolutions can be computed in near-linear randomized time O(t log^2 n). In this thesis we develop a randomized algorithm with running time O(t \log t) which is optimal (under some mild assumptions), and the first near-linear deterministic algorithm for sparse nonnegative convolution. We also present an application of these results, leading to seemingly unrelated fine-grained lower bounds against distance oracles in graphs. (2) Sublinear Edit Distance: The edit distance of two strings is a well-studied similarity measure with numerous applications in computational biology. While computing the edit distance exactly provably requires quadratic time, a long line of research has lead to a constant-factor approximation algorithm in almost-linear time. Perhaps surprisingly, it is also possible to approximate the edit distance k within a large factor O(k) in sublinear time O~(n/k + poly(k)). We drastically improve the approximation factor of the known sublinear algorithms from O(k) to k^{o(1)} while preserving the O(n/k + poly(k)) running time.In dieser Doktorarbeit über feinkörnige Algorithmen und Komplexität untersuchen wir ausgabesensitive Algorithmen und Algorithmen mit sublinearer Lauf-zeit für zwei wichtige Probleme. (1) Dünne Faltungen: Die Berechnung der Faltung zweier Vektoren ist ein grundlegendes algorithmisches Primitiv, das in allen Bereichen der Informatik und des Ingenieurwesens Anwendung findet. Für das dünne Faltungsproblem nehmen wir an, dass die Eingabe- und Ausgabevektoren höchstens t Einträge ungleich Null haben, und das Ziel ist, Algorithmen mit Laufzeiten in Abhängigkeit von t zu entwickeln. Für den speziellen Fall, dass alle Einträge nicht-negativ sind, was insbesondere für den Entwurf von Algorithmen relevant ist, ist seit zwanzig Jahren bekannt, dass dünn besetzte Faltungen in nahezu linearer randomisierter Zeit O(t \log^2 n) berechnet werden können. In dieser Arbeit entwickeln wir einen randomisierten Algorithmus mit Laufzeit O(t \log t), der (unter milden Annahmen) optimal ist, und den ersten nahezu linearen deterministischen Algorithmus für dünne nichtnegative Faltungen. Wir stellen auch eine Anwendung dieser Ergebnisse vor, die zu scheinbar unverwandten feinkörnigen unteren Schranken gegen Distanzorakel in Graphen führt. (2) Sublineare Editierdistanz: Die Editierdistanz zweier Zeichenketten ist ein gut untersuchtes Ähnlichkeitsmaß mit zahlreichen Anwendungen in der Computerbiologie. Während die exakte Berechnung der Editierdistanz nachweislich quadratische Zeit erfordert, hat eine lange Reihe von Forschungsarbeiten zu einem Approximationsalgorithmus mit konstantem Faktor in fast-linearer Zeit geführt. Überraschenderweise ist es auch möglich, die Editierdistanz k innerhalb eines großen Faktors O(k) in sublinearer Zeit O~(n/k + poly(k)) zu approximieren. Wir verbessern drastisch den Approximationsfaktor der bekannten sublinearen Algorithmen von O(k) auf k^{o(1)} unter Beibehaltung der O(n/k + poly(k))-Laufzeit

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Pushing the Boundaries of Spacecraft Autonomy and Resilience with a Custom Software Framework and Onboard Digital Twin

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    This research addresses the high CubeSat mission failure rates caused by inadequate software and overreliance on ground control. By applying a reliable design methodology to flight software development and developing an onboard digital twin platform with fault prediction capabilities, this study provides a solution to increase satellite resilience and autonomy, thus reducing the risk of mission failure. These findings have implications for spacecraft of all sizes, paving the way for more resilient space missions

    Dependent rounding with strong negative-correlation, and scheduling on unrelated machines to minimize completion time

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    We describe a new dependent-rounding algorithmic framework for bipartite graphs. Given a fractional assignment yy of values to edges of graph G=(UV,E)G = (U \cup V, E), the algorithms return an integral solution YY such that each right-node vVv \in V has at most one neighboring edge ff with Yf=1Y_f = 1, and where the variables YeY_e also satisfy broad nonpositive-correlation properties. In particular, for any edges e1,e2e_1, e_2 sharing a left-node uUu \in U, the variables Ye1,Ye2Y_{e_1}, Y_{e_2} have strong negative-correlation properties, i.e. the expectation of Ye1Ye2Y_{e_1} Y_{e_2} is significantly below ye1ye2y_{e_1} y_{e_2}. This algorithm is a refinement of a dependent-rounding algorithm of Im \& Shadloo (2020) based on simulation of Poisson processes. Our algorithm allows greater flexibility, in particular, it allows ``irregular'' fractional assignments, and it gives more refined bounds on the negative correlation. Dependent rounding schemes with negative correlation properties have been used for approximation algorithms for job-scheduling on unrelated machines to minimize weighted completion times (Bansal, Srinivasan, & Svensson (2021), Im & Shadloo (2020), Im & Li (2023)). Using our new dependent-rounding algorithm, among other improvements, we obtain a 1.4071.407-approximation for this problem. This significantly improves over the prior 1.451.45-approximation ratio of Im & Li (2023)

    24th Nordic Conference on Computational Linguistics (NoDaLiDa)

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