1,207 research outputs found
10211 Abstracts Collection -- Flexible Network Design
From Monday 24.05.2010---Friday 28.05.2010, the Dagstuhl Seminar 10211 ``Flexible Network Design \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Approximation Algorithms for Round-UFP and Round-SAP
We study Round-UFP and Round-SAP, two generalizations of the classical Bin Packing problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with capacities on its edges and a set of jobs where for each job we are given a demand and a subpath. In Round-UFP, the goal is to find a packing of all jobs into a minimum number of copies (rounds) of the given path such that for each copy, the total demand of jobs on any edge does not exceed the capacity of the respective edge. In Round-SAP, the jobs are considered to be rectangles and the goal is to find a non-overlapping packing of these rectangles into a minimum number of rounds such that all rectangles lie completely below the capacity profile of the edges.
We show that in contrast to Bin Packing, both problems do not admit an asymptotic polynomial-time approximation scheme (APTAS), even when all edge capacities are equal. However, for this setting, we obtain asymptotic (2+?)-approximations for both problems. For the general case, we obtain an O(log log n)-approximation algorithm and an O(log log 1/?)-approximation under (1+?)-resource augmentation for both problems. For the intermediate setting of the no bottleneck assumption (i.e., the maximum job demand is at most the minimum edge capacity), we obtain an absolute 12- and an asymptotic (16+?)-approximation algorithm for Round-UFP and Round-SAP, respectively
Maximum Flow on Highly Dynamic Graphs
Recent advances in dynamic graph processing have enabled the analysis of
highly dynamic graphs with change at rates as high as millions of edge changes
per second. Solutions in this domain, however, have been demonstrated only for
relatively simple algorithms like PageRank, breadth-first search, and connected
components. Expanding beyond this, we explore the maximum flow problem, a
fundamental, yet more complex problem, in graph analytics. We propose a novel,
distributed algorithm for max-flow on dynamic graphs, and implement it on top
of an asynchronous vertex-centric abstraction. We show that our algorithm can
process both additions and deletions of vertices and edges efficiently at scale
on fast-evolving graphs, and provide a comprehensive analysis by evaluating, in
addition to throughput, two criteria that are important when applied to
real-world problems: result latency and solution stability
Constraint analysis for DSP code generation
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