73 research outputs found
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Streaming Algorithms Via Reductions
In the streaming algorithms model of computation we must process data in order and without enough memory to remember the entire input. We study reductions between problems in the streaming model with an eye to using reductions as an algorithm design technique. Our contributions include:
* Linear Transformation reductions, which compose with existing linear sketch techniques. We use these for small-space algorithms for numeric measurements of distance-from-periodicity, finding the period of a numeric stream, and detecting cyclic shifts.
* The first streaming graph algorithms in the sliding window\u27 model, where we must consider only the most recent L elements for some fixed threshold L. We develop basic algorithms for connectivity and unweighted maximum matching, then develop a variety of other algorithms via reductions to these problems.
* A new reduction from maximum weighted matching to maximum unweighted matching. This reduction immediately yields improved approximation guarantees for maximum weighted matching in the semistreaming, sliding window, and MapReduce models, and extends to the more general problem of finding maximum independent sets in p-systems.
* Algorithms in a stream-of-samples model which exhibit clear sample vs. space tradeoffs. These algorithms are also inspired by examining reductions. We provide algorithms for calculating F_k frequency moments and graph connectivity
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-HĂŒbner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro PezzĂ©, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Sublinear Computation Paradigm
This open access book gives an overview of cutting-edge work on a new paradigm called the âsublinear computation paradigm,â which was proposed in the large multiyear academic research project âFoundations of Innovative Algorithms for Big Data.â That project ran from October 2014 to March 2020, in Japan. To handle the unprecedented explosion of big data sets in research, industry, and other areas of society, there is an urgent need to develop novel methods and approaches for big data analysis. To meet this need, innovative changes in algorithm theory for big data are being pursued. For example, polynomial-time algorithms have thus far been regarded as âfast,â but if a quadratic-time algorithm is applied to a petabyte-scale or larger big data set, problems are encountered in terms of computational resources or running time. To deal with this critical computational and algorithmic bottleneck, linear, sublinear, and constant time algorithms are required. The sublinear computation paradigm is proposed here in order to support innovation in the big data era. A foundation of innovative algorithms has been created by developing computational procedures, data structures, and modelling techniques for big data. The project is organized into three teams that focus on sublinear algorithms, sublinear data structures, and sublinear modelling. The work has provided high-level academic research results of strong computational and algorithmic interest, which are presented in this book. The book consists of five parts: Part I, which consists of a single chapter on the concept of the sublinear computation paradigm; Parts II, III, and IV review results on sublinear algorithms, sublinear data structures, and sublinear modelling, respectively; Part V presents application results. The information presented here will inspire the researchers who work in the field of modern algorithms
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Twin-width VIII: delineation and win-wins
We introduce the notion of delineation. A graph class is said
delineated if for every hereditary closure of a subclass of
, it holds that has bounded twin-width if and only if
is monadically dependent. An effective strengthening of
delineation for a class implies that tractable FO model checking
on is perfectly understood: On hereditary closures of
subclasses of , FO model checking is fixed-parameter tractable
(FPT) exactly when has bounded twin-width. Ordered graphs
[BGOdMSTT, STOC '22] and permutation graphs [BKTW, JACM '22] are effectively
delineated, while subcubic graphs are not. On the one hand, we prove that
interval graphs, and even, rooted directed path graphs are delineated. On the
other hand, we show that segment graphs, directed path graphs, and visibility
graphs of simple polygons are not delineated. In an effort to draw the
delineation frontier between interval graphs (that are delineated) and
axis-parallel two-lengthed segment graphs (that are not), we investigate the
twin-width of restricted segment intersection classes. It was known that
(triangle-free) pure axis-parallel unit segment graphs have unbounded
twin-width [BGKTW, SODA '21]. We show that -free segment graphs, and
axis-parallel -free unit segment graphs have bounded twin-width, where
is the half-graph or ladder of height . In contrast, axis-parallel
-free two-lengthed segment graphs have unbounded twin-width. Our new
results, combined with the known FPT algorithm for FO model checking on graphs
given with -sequences, lead to win-win arguments. For instance, we derive
FPT algorithms for -Ladder on visibility graphs of 1.5D terrains, and
-Independent Set on visibility graphs of simple polygons.Comment: 51 pages, 19 figure
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
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