IA Scholar Query: Massively Parallel Computation and Sublinear-Time Algorithms for Embedded Planar Graphs.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 21 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Massively Parallel Computation on Embedded Planar Graphs
https://scholar.archive.org/work/kruzjpzirfbsdlveqiebknildi
Many of the classic graph problems cannot be solved in the Massively Parallel Computation setting (MPC) with strongly sublinear space per machine and o(log n) rounds, unless the 1-vs-2 cycles conjecture is false. This is true even on planar graphs. Such problems include, for example, counting connected components, bipartition, minimum spanning tree problem, (approximate) shortest paths, and (approximate) diameter/radius. In this paper, we show a way to get around this limitation. Specifically, we show that if we have a "nice" (for example, straight-line) embedding of the input graph, all the mentioned problems can be solved with O(n^2/3+ϵ) space per machine in O(1) rounds. In conjunction with existing algorithms for computing the Delaunay triangulation, our results imply an MPC algorithm for exact Euclidean minimum spanning thee (EMST) that uses O(n^2/3 + ϵ) space per machine and finishes in O(1) rounds. This is the first improvement over a straightforward use of the standard Borůvka's algorithm with the Dauleanay triangulation algorithm of Goodrich [SODA 1997] which results in Θ(log n) rounds. This also partially negatively answers a question of Andoni, Nikolov, Onak, and Yaroslavtsev [STOC 2014], asking for lower bounds for exact EMST. We extend our algorithms to work with embeddings consisting of curves that are not "too squiggly" (as formalized by the total absolute curvature). We do this via a new lemma which we believe is of independent interest and could be used to parameterize other geometric problems by the total absolute curvature. We also state several open problems regarding massively parallel computation on planar graphs.Jacob Holm, Jakub Tětekwork_kruzjpzirfbsdlveqiebknildiMon, 21 Nov 2022 00:00:00 GMTParallel Breadth-First Search and Exact Shortest Paths and Stronger Notions for Approximate Distances
https://scholar.archive.org/work/b3sjg35xdjglvdmixwqpbt575q
We introduce stronger notions for approximate single-source shortest-path distances, show how to efficiently compute them from weaker standard notions, and demonstrate the algorithmic power of these new notions and transformations. One application is the first work-efficient parallel algorithm for computing exact single-source shortest paths graphs – resolving a major open problem in parallel computing. Given a source vertex in a directed graph with polynomially-bounded nonnegative integer lengths, the algorithm computes an exact shortest path tree in m log^O(1) n work and n^1/2+o(1) depth. Previously, no parallel algorithm improving the trivial linear depths of Dijkstra's algorithm without significantly increasing the work was known, even for the case of undirected and unweighted graphs (i.e., for computing a BFS-tree). Our main result is a black-box transformation that uses log^O(1) n standard approximate distance computations to produce approximate distances which also satisfy the subtractive triangle inequality (up to a (1+ε) factor) and even induce an exact shortest path tree in a graph with only slightly perturbed edge lengths. These strengthened approximations are algorithmically significantly more powerful and overcome well-known and often encountered barriers for using approximate distances. In directed graphs they can even be boosted to exact distances. This results in a black-box transformation of any (parallel or distributed) algorithm for approximate shortest paths in directed graphs into an algorithm computing exact distances at essentially no cost. Applying this to the recent breakthroughs of Fineman et al. for compute approximate SSSP-distances via approximate hopsets gives new parallel and distributed algorithm for exact shortest paths.Václav Rozhoň, Bernhard Haeupler, Anders Martinsson, Christoph Grunau, Goran Zuzicwork_b3sjg35xdjglvdmixwqpbt575qFri, 28 Oct 2022 00:00:00 GMTDigital Surveying of Large Scale Multi-Layered Terrain
https://scholar.archive.org/work/t2cgcib2ebhi7dwouvjqcmcyru
Digital terrain surveying is the exploration of terrain reconstructions and quantitative analysis of their properties. Out-of-core techniques, such as terrain streaming, are required to perform surveying on large-scale terrains at interactive frame-rates.The polyline based surveying tool from PRo3D, one of the state-of-the-art solutions for planetary geology, was implemented in our tool Visionary. In PRo3D the polylines are subsampled using fixed-rate subsampling (FRSS) at equidistant points. Our method uses variable-rate subsampling (VRSS) and shared-edge detection (SED) as an improvement that finds exact results when neighbouring primitives are hit. Furthermore, an uncertainty metric On-Data Ratio (ODR) was presented to raise awareness about the uncertainty of these measurements. Visionary was developed in the Unity game engine to evaluate if it is a suitable framework for such a specialized tool. We evaluated our implementation against Pro3D.Kevin Streicher, Michael Wimmer, Christoph Traxlerwork_t2cgcib2ebhi7dwouvjqcmcyruMon, 01 Aug 2022 00:00:00 GMTNarrowing the LOCAL-CONGEST Gaps in Sparse Networks via Expander Decompositions
https://scholar.archive.org/work/vmnckl2phjadlnsxwk6waijaeq
Many combinatorial optimization problems, including maximum weighted matching and maximum independent set, can be approximated within (1±𝜖) factors in poly(log 𝑛, 1/𝜖) rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches, however, require sending mes-Yi-Jun Chang, Hsin-Hao Suwork_vmnckl2phjadlnsxwk6waijaeqWed, 20 Jul 2022 00:00:00 GMTNarrowing the LOCALx2013CONGEST Gaps in Sparse Networks via Expander Decompositions
https://scholar.archive.org/work/ji4kagikmjaglitwxdty2fhgye
Many combinatorial optimization problems can be approximated within (1 ±ϵ) factors in poly(log n, 1/ϵ) rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches require sending messages of unlimited size, so they do not extend to the CONGEST model, which restricts the message size to be O(log n) bits. In this paper, we develop a generic framework for obtaining poly(log n, 1/ϵ)-round (1±ϵ)-approximation algorithms for many combinatorial optimization problems, including maximum weighted matching, maximum independent set, and correlation clustering, in graphs excluding a fixed minor in the CONGEST model. This class of graphs covers many sparse network classes that have been studied in the literature, including planar graphs, bounded-genus graphs, and bounded-treewidth graphs. Furthermore, we show that our framework can be applied to give an efficient distributed property testing algorithm for an arbitrary minor-closed graph property that is closed under taking disjoint union, significantly generalizing the previous distributed property testing algorithm for planarity in [Levi, Medina, and Ron, PODC 2018 Distributed Computing 2021]. Our framework uses distributed expander decomposition algorithms [Chang and Saranurak, FOCS 2020] to decompose the graph into clusters of high conductance. We show that any graph excluding a fixed minor admits small edge separators. Using this result, we show the existence of a high-degree vertex in each cluster in an expander decomposition, which allows the entire graph topology of the cluster to be routed to a vertex. Similar to the use of network decompositions in the LOCAL model, the vertex will be able to perform any local computation on the subgraph induced by the cluster and broadcast the result over the cluster.Yi-Jun Chang, Hsin-Hao Suwork_ji4kagikmjaglitwxdty2fhgyeTue, 17 May 2022 00:00:00 GMTSustaining Glasgow's Urban Networks: the Link Communities of Complex Urban Systems
https://scholar.archive.org/work/zrakggvkavc57gctqtt4w6yp5a
As cities grow in population size and became more crowded (UN DESA, 2018), the main future challenges around the world will remain to be accommodating the growing urban population while drastically reducing environmental pressure. Contemporary urban agglomerations (large or small) constantly impose burden on the natural environment by conveying ecosystem services to close and distant places, through coupled human nature [infrastructure] systems (CHANS). Tobler's first law in geography (1970) that states that "everything is related to everything else, but near things are more related than distant things" is now challenged by globalization. When this law was first established, the hypothesis referred to geological processes (Campbell and Shin, 2012, p.194) that were predominantly observed in pre-globalized economy, where freight was costly and mainly localized (Zhang et al., 2018). With the recent advances and modernisation made in transport technologies, most of them in the sea and air transportation (Zhang et al., 2018) and the growth of cities in population, natural resources and bi-products now travel great distances to infiltrate cities (Neuman, 2006) and satisfy human demands. Technical modernisation and the global hyperconnectivity of human interactions and trading, in the last thirty years alone resulted with staggering 94 per cent growth of resource extraction and consumption (Giljum et al., 2015). Local geographies (Kennedy, Cuddihy and Engel-Yan, 2007) will remain affected by global urbanisation (Giljum et al., 2015), and as a corollary, the operational inefficiencies of their local infrastructure networks, will contribute even more to the issues of environmental unsustainability on a global scale. Another challenge for future city-regions is the equity of public infrastructure services and policy creation that promote the same (Neuman and Hull, 2009). Public infrastructure services refer to services provisioned by networked infrastructure, which are subject to both public obligation and market rules. Th [...]Irena Itovawork_zrakggvkavc57gctqtt4w6yp5a