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The competitive analysis fails to model locality of reference in the online paging problem. To deal with it, Borodin et. al. introduced the access graph model, which attempts to capture the locality of reference. However, the access graph…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
Many real-world phenomena exhibit strong hierarchical structure. Consequently, in many real-world directed social networks vertices do not play equal role. Instead, vertices form a hierarchy such that the edges appear mainly from upper…
In the setting of online algorithms, the input is initially not present but rather arrive one-by-one over time and after each input, the algorithm has to make a decision. Depending on the formulation of the problem, the algorithm might be…
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively.…
For many algorithmic problems, traditional algorithms that optimise on the number of instructions executed prove expensive on I/Os. Novel and very different design techniques, when applied to these problems, can produce algorithms that are…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Graph Neural Networks (GNNs) have emerged as the leading paradigm for learning over graph-structured data. However, their performance is limited by issues inherent to graph topology, most notably oversquashing and oversmoothing. Recent…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
We develop an approach for solving rooted orienteering problems with category constraints as found in tourist trip planning and logistics. It is based on expanding partial solutions in a systematic way, prioritizing promising ones, which…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis…
In this report, we try to improve the performance of existing approaches for search operations in multi-robot context. We propose three novel algorithms that are using a triangular grid pattern, i.e., robots certainly go through the…
Deep learning models rely on highly optimized tensor libraries for efficient inference on heterogeneous hardware. Current deep compilers typically predetermine layouts of tensors and then optimize loops of operators. However, such…
Message Passing Neural Networks have recently become the most popular approach to graph machine learning tasks; however, their receptive field is limited by the number of message passing layers. To increase the receptive field, Graph…
Learning directed acyclic graphs (DAGs) to identify causal relations underlying observational data is crucial but also poses significant challenges. Recently, topology-based methods have emerged as a two-step approach to discovering DAGs by…
The performance of distributed averaging depends heavily on the underlying topology. In various fields, including compressed sensing, multi-party computation, and abstract graph theory, graphs may be expected to be free of short cycles,…
We revisit first-order optimization under local information constraints such as local privacy, gradient quantization, and computational constraints limiting access to a few coordinates of the gradient. In this setting, the optimization…
A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…
We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, (Hsu 2018) and…