166,635 research outputs found
Networks of Complements
We consider a network of sellers, each selling a single product, where the
graph structure represents pair-wise complementarities between products. We
study how the network structure affects revenue and social welfare of
equilibria of the pricing game between the sellers. We prove positive and
negative results, both of "Price of Anarchy" and of "Price of Stability" type,
for special families of graphs (paths, cycles) as well as more general ones
(trees, graphs). We describe best-reply dynamics that converge to non-trivial
equilibrium in several families of graphs, and we use these dynamics to prove
the existence of approximately-efficient equilibria.Comment: An extended abstract will appear in ICALP 201
Lombardi Drawings of Graphs
We introduce the notion of Lombardi graph drawings, named after the American
abstract artist Mark Lombardi. In these drawings, edges are represented as
circular arcs rather than as line segments or polylines, and the vertices have
perfect angular resolution: the edges are equally spaced around each vertex. We
describe algorithms for finding Lombardi drawings of regular graphs, graphs of
bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International
Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure
Encoding !-tensors as !-graphs with neighbourhood orders
Diagrammatic reasoning using string diagrams provides an intuitive language
for reasoning about morphisms in a symmetric monoidal category. To allow
working with infinite families of string diagrams, !-graphs were introduced as
a method to mark repeated structure inside a diagram. This led to !-graphs
being implemented in the diagrammatic proof assistant Quantomatic. Having a
partially automated program for rewriting diagrams has proven very useful, but
being based on !-graphs, only commutative theories are allowed. An enriched
abstract tensor notation, called !-tensors, has been used to formalise the
notion of !-boxes in non-commutative structures. This work-in-progress paper
presents a method to encode !-tensors as !-graphs with some additional
structure. This will allow us to leverage the existing code from Quantomatic
and quickly provide various tools for non-commutative diagrammatic reasoning.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Malware Classification based on Call Graph Clustering
Each day, anti-virus companies receive tens of thousands samples of
potentially harmful executables. Many of the malicious samples are variations
of previously encountered malware, created by their authors to evade
pattern-based detection. Dealing with these large amounts of data requires
robust, automatic detection approaches. This paper studies malware
classification based on call graph clustering. By representing malware samples
as call graphs, it is possible to abstract certain variations away, and enable
the detection of structural similarities between samples. The ability to
cluster similar samples together will make more generic detection techniques
possible, thereby targeting the commonalities of the samples within a cluster.
To compare call graphs mutually, we compute pairwise graph similarity scores
via graph matchings which approximately minimize the graph edit distance. Next,
to facilitate the discovery of similar malware samples, we employ several
clustering algorithms, including k-medoids and DBSCAN. Clustering experiments
are conducted on a collection of real malware samples, and the results are
evaluated against manual classifications provided by human malware analysts.
Experiments show that it is indeed possible to accurately detect malware
families via call graph clustering. We anticipate that in the future, call
graphs can be used to analyse the emergence of new malware families, and
ultimately to automate implementation of generic detection schemes.Comment: This research has been supported by TEKES - the Finnish Funding
Agency for Technology and Innovation as part of its ICT SHOK Future Internet
research programme, grant 40212/0
Asymptotically good homological error correcting codes
Let be an abstract simplicial complex. We study classical homological error correcting codes associated to , which generalize the cycle codes of simple graphs. It is well-known that cycle codes of graphs do not yield asymptotically good families of codes. We show that asymptotically good families of codes do exist for homological codes associated to simplicial complexes of dimension at least . We also prove general bounds and formulas for (co-)cycle and (co-)boundary codes for arbitrary simplicial complexes over arbitrary fields
Tensors, !-graphs, and non-commutative quantum structures
Categorical quantum mechanics (CQM) and the theory of quantum groups rely
heavily on the use of structures that have both an algebraic and co-algebraic
component, making them well-suited for manipulation using diagrammatic
techniques. Diagrams allow us to easily form complex compositions of
(co)algebraic structures, and prove their equality via graph rewriting. One of
the biggest challenges in going beyond simple rewriting-based proofs is
designing a graphical language that is expressive enough to prove interesting
properties (e.g. normal form results) about not just single diagrams, but
entire families of diagrams. One candidate is the language of !-graphs, which
consist of graphs with certain subgraphs marked with boxes (called !-boxes)
that can be repeated any number of times. New !-graph equations can then be
proved using a powerful technique called !-box induction. However, previously
this technique only applied to commutative (or cocommutative) algebraic
structures, severely limiting its applications in some parts of CQM and
(especially) quantum groups. In this paper, we fix this shortcoming by offering
a new semantics for non-commutative !-graphs using an enriched version of
Penrose's abstract tensor notation.Comment: In Proceedings QPL 2014, arXiv:1412.810
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