82 research outputs found
Finding the Minimum-Weight k-Path
Given a weighted -vertex graph with integer edge-weights taken from a
range , we show that the minimum-weight simple path visiting
vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k
M). If the weights are reals in , we provide a
-approximation which has a running time of \tilde{O}(2^k
\poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem
of -tree, in which we wish to find a minimum-weight copy of a -node tree
in a given weighted graph , under the same restrictions on edge weights
respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k)
M n^3) and a -approximate solution of running time
\tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above
algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201
Tracking advanced persistent threats in critical infrastructures through opinion dynamics
Advanced persistent threats pose a serious issue for modern industrial environments, due to their targeted and complex attack vectors that are difficult to detect. This is especially severe in critical infrastructures that are accelerating the integration of IT technologies. It is then essential to further develop effective monitoring and response systems that ensure the continuity of business to face the arising set of cyber-security threats. In this paper, we study the practical applicability of a novel technique based on opinion dynamics, that permits to trace the attack throughout all its stages along the network by correlating different anomalies measured over time, thereby taking the persistence of threats and the criticality of resources into consideration. The resulting information is of essential importance to monitor the overall health of the control system and cor- respondingly deploy accurate response procedures. Advanced Persistent Threat Detection Traceability Opinion Dynamics.Universidad de MĂĄlaga. Campus de Excelencia Internacional AndalucĂa Tech
Parameterized Algorithms for Graph Partitioning Problems
We study a broad class of graph partitioning problems, where each problem is
specified by a graph , and parameters and . We seek a subset
of size , such that is at most
(or at least) , where are constants
defining the problem, and are the cardinalities of the edge sets
having both endpoints, and exactly one endpoint, in , respectively. This
class of fixed cardinality graph partitioning problems (FGPP) encompasses Max
-Cut, Min -Vertex Cover, -Densest Subgraph, and -Sparsest
Subgraph.
Our main result is an algorithm for any problem in
this class, where is the maximum degree in the input graph.
This resolves an open question posed by Bonnet et al. [IPEC 2013]. We obtain
faster algorithms for certain subclasses of FGPPs, parameterized by , or by
. In particular, we give an time algorithm for Max
-Cut, thus improving significantly the best known time
algorithm
Preventing Advanced Persistent Threats in Complex Control Networks
An Advanced Persistent Threat (APT) is an emerging attack against Industrial Control and Automation Systems, that is executed over a long period of time and is difficult to detect. In this context, graph theory can be applied to model the interaction among nodes and the complex attacks affecting them, as well as to design recovery techniques that ensure the survivability of the network. Accordingly, we leverage a decision model to study how a set of hierarchically selected nodes can collaborate to detect an APT within the network, concerning the presence of changes in its topology. Moreover, we implement a response service based on redundant links that dynamically uses a secret sharing scheme and applies a flexible routing protocol depending on the severity of the attack. The ultimate goal is twofold: ensuring the reachability between nodes despite the changes and preventing the path followed by messages from being discovered.Universidad de MĂĄlaga. Campus de Excelencia Internacional AndalucĂa Tech
Space Saving by Dynamic Algebraization
Dynamic programming is widely used for exact computations based on tree
decompositions of graphs. However, the space complexity is usually exponential
in the treewidth. We study the problem of designing efficient dynamic
programming algorithm based on tree decompositions in polynomial space. We show
how to construct a tree decomposition and extend the algebraic techniques of
Lokshtanov and Nederlof such that the dynamic programming algorithm runs in
time , where is the maximum number of vertices in the union of
bags on the root to leaf paths on a given tree decomposition, which is a
parameter closely related to the tree-depth of a graph. We apply our algorithm
to the problem of counting perfect matchings on grids and show that it
outperforms other polynomial-space solutions. We also apply the algorithm to
other set covering and partitioning problems.Comment: 14 pages, 1 figur
Structure Theorem and Isomorphism Test for Graphs with Excluded Topological Subgraphs
We generalize the structure theorem of Robertson and Seymour for graphs
excluding a fixed graph as a minor to graphs excluding as a topological
subgraph. We prove that for a fixed , every graph excluding as a
topological subgraph has a tree decomposition where each part is either "almost
embeddable" to a fixed surface or has bounded degree with the exception of a
bounded number of vertices. Furthermore, we prove that such a decomposition is
computable by an algorithm that is fixed-parameter tractable with parameter
.
We present two algorithmic applications of our structure theorem. To
illustrate the mechanics of a "typical" application of the structure theorem,
we show that on graphs excluding as a topological subgraph, Partial
Dominating Set (find vertices whose closed neighborhood has maximum size)
can be solved in time time. More significantly, we show
that on graphs excluding as a topological subgraph, Graph Isomorphism can
be solved in time . This result unifies and generalizes two
previously known important polynomial-time solvable cases of Graph Isomorphism:
bounded-degree graphs and -minor free graphs. The proof of this result needs
a generalization of our structure theorem to the context of invariant treelike
decomposition
On -Simple -Path
An -simple -path is a {path} in the graph of length that passes
through each vertex at most times. The -SIMPLE -PATH problem, given a
graph as input, asks whether there exists an -simple -path in . We
first show that this problem is NP-Complete. We then show that there is a graph
that contains an -simple -path and no simple path of length greater
than . So this, in a sense, motivates this problem especially
when one's goal is to find a short path that visits many vertices in the graph
while bounding the number of visits at each vertex.
We then give a randomized algorithm that runs in time that solves the -SIMPLE -PATH on a graph with
vertices with one-sided error. We also show that a randomized algorithm
with running time with gives a
randomized algorithm with running time \poly(n)\cdot 2^{cn} for the
Hamiltonian path problem in a directed graph - an outstanding open problem. So
in a sense our algorithm is optimal up to an factor
How to make ecological models useful for environmental management
Understanding and predicting the ecological consequences of different management alternatives is becoming increasingly important to support environmental management decisions. Ecological models could contribute to such predictions, but in the past this was often not the case. Ecological models are often developed within research projects but are rarely used for practical applications. In this synthesis paper, we discuss how to strengthen the role of ecological modeling in supporting environmental management decisions with a focus on methodological aspects. We address mainly ecological modellers but also potential users of modeling results. Various modeling approaches can be used to predict the response of ecosystems to anthropogenic interventions, including mechanistic models, statistical models, and machine learning approaches. Regardless of the chosen approach, we outline how to better align the modeling to the decision making process, and identify six requirements that we believe are important to increase the usefulness of ecological models for management support, especially if management decisions need to be justified to the public. These cover: (i) a mechanistic understanding regarding causality, (ii) alignment of model input and output with the management decision, (iii) appropriate spatial and temporal resolutions, (iv) uncertainty quantification, (v) sufficient predictive performance, and (vi) transparent communication. We discuss challenges and synthesize suggestions for addressing these points. © 2019 The Author(s)This paper was initialized during a special session on Ecological Modelling at the 10th Symposium for European Freshwater Science 2017 ( http://www.sefs10.cz/ ) and further developed during the AQUACROSS project, funded by European Union's Horizon 2020 research and innovation programme (Grant agreement No. 642317 ). SD, SDL and MF were partly funded by the âGLANCEâ project (Global Change Effects in River Ecosystems; 01 LN1320A) through the German Federal Ministry of Education and Research ( BMBF ). SDL has received additional funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 748625 . JML acknowledges the support of the Spanish Government through MarĂa de Maeztu excellence accreditation 2018â2021 (Ref. MDM-2017-0714 )
Parameterized and Approximation Algorithms for the Load Coloring Problem
Let be two positive integers and let be a graph. The
-Load Coloring Problem (denoted -LCP) asks whether there is a
-coloring such that for every ,
there are at least edges with both endvertices colored . Gutin and Jones
(IPL 2014) studied this problem with . They showed -LCP to be fixed
parameter tractable (FPT) with parameter by obtaining a kernel with at most
vertices. In this paper, we extend the study to any fixed by giving
both a linear-vertex and a linear-edge kernel. In the particular case of ,
we obtain a kernel with less than vertices and less than edges. These
results imply that for any fixed , -LCP is FPT and that the
optimization version of -LCP (where is to be maximized) has an
approximation algorithm with a constant ratio for any fixed
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