Related papers: Verifying Graph Algorithms in Separation Logic: A …
In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of resources---a form of state transition system---to describe the state-based program…
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
In this paper, we prove intractability results about sampling from the set of partitions of a planar graph into connected components. Our proofs are motivated by a technique introduced by Jerrum, Valiant, and Vazirani. Moreover, we use…
We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
The mim-width of a graph is a powerful structural parameter that, when bounded by a constant, allows several hard problems to be polynomial-time solvable - with a recent meta-theorem encompassing a large class of problems [SODA2023]. Since…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…
Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…
Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…