48,853 research outputs found
A practical fpt algorithm for Flow Decomposition and transcript assembly
The Flow Decomposition problem, which asks for the smallest set of weighted
paths that "covers" a flow on a DAG, has recently been used as an important
computational step in transcript assembly. We prove the problem is in FPT when
parameterized by the number of paths by giving a practical linear fpt
algorithm. Further, we implement and engineer a Flow Decomposition solver based
on this algorithm, and evaluate its performance on RNA-sequence data.
Crucially, our solver finds exact solutions while achieving runtimes
competitive with a state-of-the-art heuristic. Finally, we contextualize our
design choices with two hardness results related to preprocessing and weight
recovery. Specifically, -Flow Decomposition does not admit polynomial
kernels under standard complexity assumptions, and the related problem of
assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0.
http://dx.doi.org/10.5281/zenodo.82163
Pseudo-Separation for Assessment of Structural Vulnerability of a Network
Based upon the idea that network functionality is impaired if two nodes in a
network are sufficiently separated in terms of a given metric, we introduce two
combinatorial \emph{pseudocut} problems generalizing the classical min-cut and
multi-cut problems. We expect the pseudocut problems will find broad relevance
to the study of network reliability. We comprehensively analyze the
computational complexity of the pseudocut problems and provide three
approximation algorithms for these problems.
Motivated by applications in communication networks with strict
Quality-of-Service (QoS) requirements, we demonstrate the utility of the
pseudocut problems by proposing a targeted vulnerability assessment for the
structure of communication networks using QoS metrics; we perform experimental
evaluations of our proposed approximation algorithms in this context
A Polynomial-time Bicriteria Approximation Scheme for Planar Bisection
Given an undirected graph with edge costs and node weights, the minimum
bisection problem asks for a partition of the nodes into two parts of equal
weight such that the sum of edge costs between the parts is minimized. We give
a polynomial time bicriteria approximation scheme for bisection on planar
graphs.
Specifically, let be the total weight of all nodes in a planar graph .
For any constant , our algorithm outputs a bipartition of the
nodes such that each part weighs at most and the total cost
of edges crossing the partition is at most times the total
cost of the optimal bisection. The previously best known approximation for
planar minimum bisection, even with unit node weights, was . Our
algorithm actually solves a more general problem where the input may include a
target weight for the smaller side of the bipartition.Comment: To appear in STOC 201
Setting Parameters by Example
We introduce a class of "inverse parametric optimization" problems, in which
one is given both a parametric optimization problem and a desired optimal
solution; the task is to determine parameter values that lead to the given
solution. We describe algorithms for solving such problems for minimum spanning
trees, shortest paths, and other "optimal subgraph" problems, and discuss
applications in multicast routing, vehicle path planning, resource allocation,
and board game programming.Comment: 13 pages, 3 figures. To be presented at 40th IEEE Symp. Foundations
of Computer Science (FOCS '99
Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints
For a given graph with positive integral cost and delay on edges,
distinct vertices and , cost bound and delay bound , the bi-constraint path (BCP) problem is to compute disjoint
-paths subject to and . This problem is known NP-hard, even when
\cite{garey1979computers}. This paper first gives a simple approximation
algorithm with factor-, i.e. the algorithm computes a solution with
delay and cost bounded by and respectively. Later, a novel improved
approximation algorithm with ratio
is developed by constructing
interesting auxiliary graphs and employing the cycle cancellation method. As a
consequence, we can obtain a factor- approximation algorithm by
setting and a factor- algorithm by
setting . Besides, by setting , an
approximation algorithm with ratio , i.e. an algorithm with
only a single factor ratio on cost, can be immediately obtained. To
the best of our knowledge, this is the first non-trivial approximation
algorithm for the BCP problem that strictly obeys the delay constraint.Comment: 12 page
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