1,432 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
A tamed family of triangle-free graphs with unbounded chromatic number
We construct a hereditary class of triangle-free graphs with unbounded
chromatic number, in which every non-trivial graph either contains a pair of
non-adjacent twins or has an edgeless vertex cutset of size at most two. This
answers in the negative a question of Chudnovsky, Penev, Scott, and Trotignon.
The class is the hereditary closure of a family of (triangle-free) twincut
graphs such that has chromatic number . We also
show that every twincut graph is edge-critical
Mining Butterflies in Streaming Graphs
This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection.
sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals
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
Thick Forests
We consider classes of graphs, which we call thick graphs, that have their
vertices replaced by cliques and their edges replaced by bipartite graphs. In
particular, we consider the case of thick forests, which are a subclass of
perfect graphs. We show that this class can be recognised in polynomial time,
and examine the complexity of counting independent sets and colourings for
graphs in the class. We consider some extensions of our results to thick graphs
beyond thick forests.Comment: 40 pages, 19 figure
Recontamination Helps a Lot to Hunt a Rabbit
The Hunters and Rabbit game is played on a graph G where the Hunter player shoots at k vertices in every round while the Rabbit player occupies an unknown vertex and, if it is not shot, must move to a neighbouring vertex after each round. The Rabbit player wins if it can ensure that its position is never shot. The Hunter player wins otherwise. The hunter number h(G) of a graph G is the minimum integer k such that the Hunter player has a winning strategy (i.e., allowing him to win whatever be the strategy of the Rabbit player). This game has been studied in several graph classes, in particular in bipartite graphs (grids, trees, hypercubes...), but the computational complexity of computing h(G) remains open in general graphs and even in more restricted graph classes such as trees. To progress further in this study, we propose a notion of monotonicity (a well-studied and useful property in classical pursuit-evasion games such as Graph Searching games) for the Hunters and Rabbit game imposing that, roughly, a vertex that has already been shot "must not host the rabbit anymore". This allows us to obtain new results in various graph classes.
More precisely, let the monotone hunter number mh(G) of a graph G be the minimum integer k such that the Hunter player has a monotone winning strategy. We show that pw(G) ? mh(G) ? pw(G)+1 for any graph G with pathwidth pw(G), which implies that computing mh(G), or even approximating mh(G) up to an additive constant, is NP-hard. Then, we show that mh(G) can be computed in polynomial time in split graphs, interval graphs, cographs and trees. These results go through structural characterisations which allow us to relate the monotone hunter number with the pathwidth in some of these graph classes. In all cases, this allows us to specify the hunter number or to show that there may be an arbitrary gap between h and mh, i.e., that monotonicity does not help. In particular, we show that, for every k ? 3, there exists a tree T with h(T) = 2 and mh(T) = k. We conclude by proving that computing h (resp., mh) is FPT parameterised by the minimum size of a vertex cover
Hereditary classes of graphs : a parametric approach
The world of hereditary classes is rich and diverse and it contains a variety of classes of theoretical and practical importance. Thousands of results in the literature are devoted to individual classes and only a few of them analyse the universe of hereditary classes as a whole. To shift the analysis into a new level, in the present paper we exploit an approach, where we operate by infinite families of classes, rather than individual classes. Each family is associated with a graph parameter and is characterized by classes that are critical with respect to the parameter. In particular, we obtain a complete parametric description of the bottom of the lattice of hereditary classes and discuss a number of open questions related to this approach
Geometric Learning on Graph Structured Data
Graphs provide a ubiquitous and universal data structure that can be applied in many domains such as social networks, biology, chemistry, physics, and computer science. In this thesis we focus on two fundamental paradigms in graph learning: representation learning and similarity learning over graph-structured data. Graph representation learning aims to learn embeddings for nodes by integrating topological and feature information of a graph. Graph similarity learning brings into play with similarity functions that allow to compute similarity between pairs of graphs in a vector space. We address several challenging issues in these two paradigms, designing powerful, yet efficient and theoretical guaranteed machine learning models that can leverage rich topological structural properties of real-world graphs.
This thesis is structured into two parts. In the first part of the thesis, we will present how to develop powerful Graph Neural Networks (GNNs) for graph representation learning from three different perspectives: (1) spatial GNNs, (2) spectral GNNs, and (3) diffusion GNNs. We will discuss the model architecture, representational power, and convergence properties of these GNN models. Specifically, we first study how to develop expressive, yet efficient and simple message-passing aggregation schemes that can go beyond the Weisfeiler-Leman test (1-WL). We propose a generalized message-passing framework by incorporating graph structural properties into an aggregation scheme. Then, we introduce a new local isomorphism hierarchy on neighborhood subgraphs. We further develop a novel neural model, namely GraphSNN, and theoretically prove that this model is more expressive than the 1-WL test. After that, we study how to build an effective and efficient graph convolution model with spectral graph filters. In this study, we propose a spectral GNN model, called DFNets, which incorporates a novel spectral graph filter, namely feedback-looped filters. As a result, this model can provide better localization on neighborhood while achieving fast convergence and linear memory requirements. Finally, we study how to capture the rich topological information of a graph using graph diffusion. We propose a novel GNN architecture with dynamic PageRank, based on a learnable transition matrix. We explore two variants of this GNN architecture: forward-euler solution and invariable feature solution, and theoretically prove that our forward-euler GNN architecture is guaranteed with the convergence to a stationary distribution.
In the second part of this thesis, we will introduce a new optimal transport distance metric on graphs in a regularized learning framework for graph kernels. This optimal transport distance metric can preserve both local and global structures between graphs during the transport, in addition to preserving features and their local variations. Furthermore, we propose two strongly convex regularization terms to theoretically guarantee the convergence and numerical stability in finding an optimal assignment between graphs. One regularization term is used to regularize a Wasserstein distance between graphs in the same ground space. This helps to preserve the local clustering structure on graphs by relaxing the optimal transport problem to be a cluster-to-cluster assignment between locally connected vertices. The other regularization term is used to regularize a Gromov-Wasserstein distance between graphs across different ground spaces based on degree-entropy KL divergence. This helps to improve the matching robustness of an optimal alignment to preserve the global connectivity structure of graphs. We have evaluated our optimal transport-based graph kernel using different benchmark tasks. The experimental results show that our models considerably outperform all the state-of-the-art methods in all benchmark tasks
Parameterized Complexity of Fair Bisection: FPT-Approximation meets Unbreakability
In the Minimum Bisection problem, input is a graph and the goal is to
partition the vertex set into two parts and , such that and the number of edges between and is minimized. This problem
can be viewed as a clustering problem where edges represent similarity, and the
task is to partition the vertices into two equally sized clusters, while
minimizing the number of pairs of similar objects that end up in different
clusters. In this paper, we initiate the study of a fair version of Minimum
Bisection. In this problem, the vertices of the graph are colored using one of
colors. The goal is to find a bisection with at most
edges between the parts, such that for each color , has exactly
vertices of color .
We first show that Fair Bisection is [1]-hard parameterized by even
when . On the other hand, our main technical contribution shows that is
that this hardness result is simply a consequence of the very strict
requirement that each color class has {\em exactly} vertices in .
In particular, we give an time algorithm that finds a
balanced partition with at most edges between them, such that for
each color , there are at most vertices of color
in . Our approximation algorithm is best viewed as a proof of concept
that the technique introduced by [Lampis, ICALP '18] for obtaining
FPT-approximation algorithms for problems of bounded tree-width or clique-width
can be efficiently exploited even on graphs of unbounded width. The key insight
is that the technique of Lampis is applicable on tree decompositions with
unbreakable bags (as introduced in [Cygan et al., SIAM Journal on Computing
'14]). Along the way, we also derive a combinatorial result regarding tree
decompositions of graphs.Comment: Full version of ESA 2023 paper. Abstract shortened to meet the
character limi
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