1,238 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Computing complexity measures of degenerate graphs
We show that the VC-dimension of a graph can be computed in time , where is the degeneracy of the input graph. The core idea
of our algorithm is a data structure to efficiently query the number of
vertices that see a specific subset of vertices inside of a (small) query set.
The construction of this data structure takes time , afterwards
queries can be computed efficiently using fast M\"obius inversion.
This data structure turns out to be useful for a range of tasks, especially
for finding bipartite patterns in degenerate graphs, and we outline an
efficient algorithms for counting the number of times specific patterns occur
in a graph. The largest factor in the running time of this algorithm is
, where is a parameter of the pattern we call its left covering
number.
Concrete applications of this algorithm include counting the number of
(non-induced) bicliques in linear time, the number of co-matchings in quadratic
time, as well as a constant-factor approximation of the ladder index in linear
time.
Finally, we supplement our theoretical results with several implementations
and run experiments on more than 200 real-world datasets -- the largest of
which has 8 million edges -- where we obtain interesting insights into the
VC-dimension of real-world networks.Comment: Accepted for publication in the 18th International Symposium on
Parameterized and Exact Computation (IPEC 2023
On Diameter Approximation in Directed Graphs
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs. approximation trade-off that is quite close to the upper bounds.
In directed graphs, however, where only some of the upper bounds apply, much larger gaps remain. Since d(u,v) may not be the same as d(v,u), there are multiple ways to define the problem, the two most natural being the (one-way) diameter (max_(u,v) d(u,v)) and the roundtrip diameter (max_{u,v} d(u,v)+d(v,u)). In this paper we make progress on the outstanding open question for each of them.
- We design the first algorithm for diameter in sparse directed graphs to achieve n^{1.5-?} time with an approximation factor better than 2. The new upper bound trade-off makes the directed case appear more similar to the undirected case. Notably, this is the first algorithm for diameter in sparse graphs that benefits from fast matrix multiplication.
- We design new hardness reductions separating roundtrip diameter from directed and undirected diameter. In particular, a 1.5-approximation in subquadratic time would refute the All-Nodes k-Cycle hypothesis, and any (2-?)-approximation would imply a breakthrough algorithm for approximate ?_?-Closest-Pair. Notably, these are the first conditional lower bounds for diameter that are not based on SETH
Searching for Dead Sea Scribes:a study on using Artificial Intelligence and palaeography for writer identification in correlation with spelling and scribal practices, codicology, handwriting quality, and literary classification systems for Dead Sea Scrolls
My study explores the Dead Sea Scrolls through the lens of individual scribes. Specifically, the practices of individual scribes responsible for penningtwo or more of the Oumran manuscripts. It utilises innovative digital palaeographic methods alongside traditional palaeographic approaches for scribalidentification. It gathers previously un-gathered data on the handwriting, spelling practices, codicological features and literary content of individual scribes. The study explores how this data on scribes both supports and challenges various aspects of theories in the field of Dead Sea Scroll studies, which accept a a sectarian origin for the Qumran manuscripts
Computational Approaches to Drug Profiling and Drug-Protein Interactions
Despite substantial increases in R&D spending within the pharmaceutical industry, denovo drug design has become a time-consuming endeavour. High attrition rates led to a
long period of stagnation in drug approvals. Due to the extreme costs associated with
introducing a drug to the market, locating and understanding the reasons for clinical failure
is key to future productivity. As part of this PhD, three main contributions were made in
this respect. First, the web platform, LigNFam enables users to interactively explore
similarity relationships between ‘drug like’ molecules and the proteins they bind. Secondly,
two deep-learning-based binding site comparison tools were developed, competing with
the state-of-the-art over benchmark datasets. The models have the ability to predict offtarget interactions and potential candidates for target-based drug repurposing. Finally, the
open-source ScaffoldGraph software was presented for the analysis of hierarchical scaffold
relationships and has already been used in multiple projects, including integration into a
virtual screening pipeline to increase the tractability of ultra-large screening experiments.
Together, and with existing tools, the contributions made will aid in the understanding of
drug-protein relationships, particularly in the fields of off-target prediction and drug
repurposing, helping to design better drugs faster
Realizing temporal graphs from fastest travel times
In this paper we initiate the study of the \emph{temporal graph realization}
problem with respect to the fastest path durations among its vertices, while we
focus on periodic temporal graphs. Given an matrix and a
, the goal is to construct a -periodic temporal
graph with vertices such that the duration of a \emph{fastest path} from
to is equal to , or to decide that such a temporal graph
does not exist. The variations of the problem on static graphs has been well
studied and understood since the 1960's, and this area of research remains
active until nowadays.
As it turns out, the periodic temporal graph realization problem has a very
different computational complexity behavior than its static (i.e. non-temporal)
counterpart. First we show that the problem is NP-hard in general, but
polynomial-time solvable if the so-called underlying graph is a tree or a
cycle. Building upon those results, we investigate its parameterized
computational complexity with respect to structural parameters of the
underlying static graph which measure the ``tree-likeness''. For those
parameters, we essentially give a tight classification between parameters that
allow for tractability (in the FPT sense) and parameters that presumably do
not. We show that our problem is W[1]-hard when parameterized by the
\emph{feedback vertex number} of the underlying graph, while we show that it is
in FPT when parameterized by the \emph{feedback edge number} of the underlying
graph.Comment: 57 pages, 10 figure
Entity Linking for the Biomedical Domain
Entity linking is the process of detecting mentions of different concepts in text documents and linking them to canonical entities in a target lexicon.
However, one of the biggest issues in entity linking is the ambiguity in entity names. The ambiguity is an issue that many text mining tools have yet to address since different names can represent the same thing and every mention could indicate a different thing. For instance, search engines that rely on heuristic string matches frequently return irrelevant results, because they are unable to satisfactorily resolve ambiguity.
Thus, resolving named entity ambiguity is a crucial step in entity linking. To solve the problem of ambiguity,
this work proposes a heuristic method for entity recognition and entity linking over the biomedical knowledge graph concerning the semantic similarity of entities in the knowledge graph. Named entity recognition (NER), relation extraction (RE), and relationship linking make up a conventional entity linking (EL) system pipeline (RL). We have used the accuracy metric in this thesis.
Therefore, for each identified relation or entity, the solution comprises identifying the correct one and matching it to its corresponding unique CUI in the knowledge base. Because KBs contain a substantial number of relations and entities, each with only one natural language label, the second phase is directly dependent on the accuracy of the first. The framework developed in this thesis enables the extraction of relations and entities from the text and their mapping to the associated CUI in the UMLS knowledge base. This approach derives a new representation of the knowledge base that lends it to the easy comparison. Our idea to select the best candidates is to build a graph of relations and determine the shortest path distance using a ranking approach.
We test our suggested approach on two well-known benchmarks in the biomedical field and show that our method exceeds the search engine's top result and provides us with around 4% more accuracy. In general, when it comes to fine-tuning, we notice that entity linking contains subjective characteristics and modifications may be required depending on the task at hand. The performance of the framework is evaluated based on a Python implementation
Quantum Algorithm for Maximum Biclique Problem
Identifying a biclique with the maximum number of edges bears considerable
implications for numerous fields of application, such as detecting anomalies in
E-commerce transactions, discerning protein-protein interactions in biology,
and refining the efficacy of social network recommendation algorithms. However,
the inherent NP-hardness of this problem significantly complicates the matter.
The prohibitive time complexity of existing algorithms is the primary
bottleneck constraining the application scenarios. Aiming to address this
challenge, we present an unprecedented exploration of a quantum computing
approach. Efficient quantum algorithms, as a crucial future direction for
handling NP-hard problems, are presently under intensive investigation, of
which the potential has already been proven in practical arenas such as
cybersecurity. However, in the field of quantum algorithms for graph databases,
little work has been done due to the challenges presented by the quantum
representation of complex graph topologies. In this study, we delve into the
intricacies of encoding a bipartite graph on a quantum computer. Given a
bipartite graph with n vertices, we propose a ground-breaking algorithm qMBS
with time complexity O^*(2^(n/2)), illustrating a quadratic speed-up in terms
of complexity compared to the state-of-the-art. Furthermore, we detail two
variants tailored for the maximum vertex biclique problem and the maximum
balanced biclique problem. To corroborate the practical performance and
efficacy of our proposed algorithms, we have conducted proof-of-principle
experiments utilizing IBM quantum simulators, of which the results provide a
substantial validation of our approach to the extent possible to date
Change and continuity at the Roman coastal fort at Oudenburg from the late 2nd until the early 5th century AD. Volume I: The site and its significance within the wider context of the Roman North Sea and Channel frontier zone
In de latere Romeinse periode vormde de Noordzee- en Kanaalregio het decor voor aanvallen van over zee, politieke crisissen, hervormingen van het leger, Germaanse invallen en veranderende verdedigingsstrategieën van het Romeinse Rijk. Woelige tijden dus, waarover weinig literaire bronnen bestaan. De kustforten zijn van onschatbare waarde om de gebeurtenissen van deze periode te begrijpen, maar onderzoek daarvan was schaars. De opgravingen van het Oudenburgse castellum zorgden dan ook voor een belangrijke ommezwaai in onze kennis over die gebeurtenissen, want ze bieden een unieke inkijk in het enige gekende Romeinse stenen fort in Vlaanderen.
De opgravingen legden een opmerkelijk goed bewaarde chronologie bloot van vijf opeenvolgende forten, van de late 2de tot de vroege 5de eeuw na Chr. Het is de eerste keer in een kustfort dat de evolutie van midden- tot laat-Romeins fort zo precies kan gedateerd en geïllustreerd worden. Politieke, economische en sociale ontwikkelingen zijn duidelijk te herkennen, dankzij de uitgebreide studie van de stratigrafie en de enorme hoeveelheid aan vondsten. De materiaalstudies, uitgevoerd door specialisten die gebruik maken van verschillende analytische methodes, vormen referenties voor regionaal militair onderzoek en studies van de latere Romeinse periode in de noordwestelijke provincies.
De studie van het kustfort van Oudenburg helpt het onderzoek naar verandering en continuïteit en identiteit met betrekking tot het dagelijks leven van de soldaten en de interactie met de ruimere regio. Het is duidelijk dat dit castellum nauw verbonden was met de Britse forten, de Germaanse invloed er geleidelijk aan toenam en het leven in het fort evolueerde naar dat van een gemeenschap van militaire families
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