1,839 research outputs found
Transit Node Routing Reconsidered
Transit Node Routing (TNR) is a fast and exact distance oracle for road
networks. We show several new results for TNR. First, we give a surprisingly
simple implementation fully based on Contraction Hierarchies that speeds up
preprocessing by an order of magnitude approaching the time for just finding a
CH (which alone has two orders of magnitude larger query time). We also develop
a very effective purely graph theoretical locality filter without any
compromise in query times. Finally, we show that a specialization to the online
many-to-one (or one-to-many) shortest path further speeds up query time by an
order of magnitude. This variant even has better query time than the fastest
known previous methods which need much more space.Comment: 19 pages, submitted to SEA'201
Trip-Based Public Transit Routing Using Condensed Search Trees
We study the problem of planning Pareto-optimal journeys in public transit
networks. Most existing algorithms and speed-up techniques work by computing
subjourneys to intermediary stops until the destination is reached. In
contrast, the trip-based model focuses on trips and transfers between them,
constructing journeys as a sequence of trips. In this paper, we develop a
speed-up technique for this model inspired by principles behind existing
state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The
resulting algorithm allows us to compute Pareto-optimal (with respect to
arrival time and number of transfers) 24-hour profiles on very large real-world
networks in less than half a millisecond. Compared to the current state of the
art for bicriteria queries on public transit networks, this is up to two orders
of magnitude faster, while increasing preprocessing overhead by at most one
order of magnitude
The Cost of Address Translation
Modern computers are not random access machines (RAMs). They have a memory
hierarchy, multiple cores, and virtual memory. In this paper, we address the
computational cost of address translation in virtual memory. Starting point for
our work is the observation that the analysis of some simple algorithms (random
scan of an array, binary search, heapsort) in either the RAM model or the EM
model (external memory model) does not correctly predict growth rates of actual
running times. We propose the VAT model (virtual address translation) to
account for the cost of address translations and analyze the algorithms
mentioned above and others in the model. The predictions agree with the
measurements. We also analyze the VAT-cost of cache-oblivious algorithms.Comment: A extended abstract of this paper was published in the proceedings of
ALENEX13, New Orleans, US
Route Planning in Transportation Networks
We survey recent advances in algorithms for route planning in transportation
networks. For road networks, we show that one can compute driving directions in
milliseconds or less even at continental scale. A variety of techniques provide
different trade-offs between preprocessing effort, space requirements, and
query time. Some algorithms can answer queries in a fraction of a microsecond,
while others can deal efficiently with real-time traffic. Journey planning on
public transportation systems, although conceptually similar, is a
significantly harder problem due to its inherent time-dependent and
multicriteria nature. Although exact algorithms are fast enough for interactive
queries on metropolitan transit systems, dealing with continent-sized instances
requires simplifications or heavy preprocessing. The multimodal route planning
problem, which seeks journeys combining schedule-based transportation (buses,
trains) with unrestricted modes (walking, driving), is even harder, relying on
approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4,
previously published by Microsoft Research. This work was mostly done while
the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at
Microsoft Research Silicon Valle
Trip-Based Public Transit Routing
We study the problem of computing all Pareto-optimal journeys in a public
transit network regarding the two criteria of arrival time and number of
transfers taken. We take a novel approach, focusing on trips and transfers
between them, allowing fine-grained modeling. Our experiments on the
metropolitan network of London show that the algorithm computes full 24-hour
profiles in 70 ms after a preprocessing phase of 30 s, allowing fast queries in
dynamic scenarios.Comment: Minor corrections, no substantial changes. To be presented at ESA
201
Python for education: the exact cover problem
Python implementation of Algorithm X by Knuth is presented. Algorithm X finds
all solutions to the exact cover problem. The exemplary results for
pentominoes, Latin squares and Sudoku are given.Comment: 13 pages, 4 figures, 3 table
Correlating Theory and Practice in Finding Clubs and Plexes
For solving NP-hard problems there is often a huge gap between theoretical guarantees and observed running times on real-world instances. As a first step towards tackling this issue, we propose an approach to quantify the correlation between theoretical and observed running times.
We use two NP-hard problems related to finding large "cliquish" subgraphs in a given graph as demonstration of this measure. More precisely, we focus on finding maximum s-clubs and s-plexes, i. e., graphs of diameter s and graphs where each vertex is adjacent to all but s vertices. Preprocessing based on Turing kernelization is a standard tool to tackle these problems, especially on sparse graphs. We provide a parameterized analysis for the Turing kernelization and demonstrate their usefulness in practice. Moreover, we demonstrate that our measure indeed captures the correlation between these new theoretical and the observed running times
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