518 research outputs found
Quasi-kernels in split graphs
In a digraph, a quasi-kernel is a subset of vertices that is independent and
such that the shortest path from every vertex to this subset is of length at
most two. The ``small quasi-kernel conjecture,'' proposed by Erd\H{o}s and
Sz\'ekely in 1976, postulates that every sink-free digraph has a quasi-kernel
whose size is within a fraction of the total number of vertices. The conjecture
is even more precise with a ratio, but even with larger ratio, this
property is known to hold only for few classes of graphs. The focus here is on
small quasi-kernels in split graphs. This family of graphs has played a special
role in the study of the conjecture since it was used to disprove a
strengthening that postulated the existence of two disjoint quasi-kernels. The
paper proves that every sink-free split digraph has a quasi-kernel of size
at most , and even of size at most two when the graph is an
orientation of a complete split graph. It is also shown that computing a
quasi-kernel of minimal size in a split digraph is W[2]-hard
On the Small Quasi-kernel conjecture
The Chv\'atal-Lov\'asz theorem from 1974 establishes in every finite digraph
the existence of a quasi-kernel, i.e., an independent -out-dominating
vertex set. In the same spirit, the Small Quasi-kernel Conjecture, proposed by
Erd\H{o}s and Sz\'ekely in 1976, asserts the existence of a quasi-kernel of
order at most if does not have sources. Despite repeated
efforts, the conjecture remains wide open.
This work contains a number of new results towards the conjecture. In our
main contribution we resolve the conjecture for all directed graphs without
sources containing a kernel in the second out-neighborhood of a quasi-kernel.
Furthermore, we provide a novel strongly connected example demonstrating the
asymptotic sharpness of the conjecture. Additionally, we resolve the conjecture
in a strong form for all directed unicyclic graphs.Comment: 12 pages, 1 figur
A Multi-view Context-aware Approach to Android Malware Detection and Malicious Code Localization
Existing Android malware detection approaches use a variety of features such
as security sensitive APIs, system calls, control-flow structures and
information flows in conjunction with Machine Learning classifiers to achieve
accurate detection. Each of these feature sets provides a unique semantic
perspective (or view) of apps' behaviours with inherent strengths and
limitations. Meaning, some views are more amenable to detect certain attacks
but may not be suitable to characterise several other attacks. Most of the
existing malware detection approaches use only one (or a selected few) of the
aforementioned feature sets which prevent them from detecting a vast majority
of attacks. Addressing this limitation, we propose MKLDroid, a unified
framework that systematically integrates multiple views of apps for performing
comprehensive malware detection and malicious code localisation. The rationale
is that, while a malware app can disguise itself in some views, disguising in
every view while maintaining malicious intent will be much harder.
MKLDroid uses a graph kernel to capture structural and contextual information
from apps' dependency graphs and identify malice code patterns in each view.
Subsequently, it employs Multiple Kernel Learning (MKL) to find a weighted
combination of the views which yields the best detection accuracy. Besides
multi-view learning, MKLDroid's unique and salient trait is its ability to
locate fine-grained malice code portions in dependency graphs (e.g.,
methods/classes). Through our large-scale experiments on several datasets
(incl. wild apps), we demonstrate that MKLDroid outperforms three
state-of-the-art techniques consistently, in terms of accuracy while
maintaining comparable efficiency. In our malicious code localisation
experiments on a dataset of repackaged malware, MKLDroid was able to identify
all the malice classes with 94% average recall
Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
In a complex system the interplay between the internal structure of its
entities and their interconnection may play a fundamental role in the global
functioning of the system. Here, we define the concept of metaplex, which
describes such trade-off between internal structure of entities and their
interconnections. We then define a dynamical system on a metaplex and study
diffusive processes on them. We provide analytical and computational evidences
about the role played by the size of the nodes, the location of the internal
coupling areas, and the strength and range of the coupling between the nodes on
the global dynamics of metaplexes. Finally, we extend our analysis to two
real-world metaplexes: a landscape and a brain metaplex. We corroborate that
the internal structure of the nodes in a metaplex may dominate the global
dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the
influence of the interconnection between nodes.Comment: 28 pages, 19 figure
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