Project description
Linear-time algorithms to solve fundamental graph problems
Real-world systems like road networks and social networks can be represented as graphs – structures made of points (vertices) connected by lines (edges). Solving problems on graphs, such as finding weak points or breaking them into smaller parts, is crucial in computer science. However, some fundamental problems still lack optimal solutions. With the support of the Marie Skłodowska-Curie Actions programme, the KCONN project aims to create optimal, linear-time algorithms for key graph challenges, such as identifying small edge cuts and calculating treewidth – a measure of graph complexity. By combining new techniques from structural graph theory, the proposed study could help solve long-standing challenges and advance the field of graph algorithms significantly.
Objective
Graphs are structures consisting of vertices (points) and edges (lines connecting pairs of points). Graphs can model systems such as road networks (intersections connected by roads), social networks (people connected by friendships), and the internet (computers connected by data links). The design of efficient algorithms for processing graphs is a classic area in computer science. However, there are still fundamental graph problems for which optimal algorithms remain undiscovered.
This project aims to design optimal algorithms and data structures for solving graph problems related to finding small cuts or separators and decomposing graphs accordingly. A basic example of a graph problem where I aim to advance the state-of-the-art is: Given a graph, determine whether it can be disconnected by removing at most 10 edges. The best-known algorithm runs in near-linear O(n log n + m) time, while the goal of this project is to obtain a linear-time O(n+m) algorithm, which is optimal. The specific number 10 is not important; rather, the goal is to develop a linear-time algorithm for any fixed value, in the spirit of parameterized algorithms.
The research objectives are (1) to develop a linear-time algorithm for computing the k-edge-connected components of a graph, (2) to create an improved dynamic data structure for treewidth, and (3) to design a linear-time preprocessing algorithm for computing treewidth. Objective (1) addresses a long-standing open problem in graph algorithms, while objectives (2) and (3) will significantly advance the state-of-the-art in key problems within parameterized algorithms. I believe I have identified a feasible approach to tackling these problems, introducing new techniques from structural graph theory into algorithm design.
Solving a key open problem in graph algorithms using tools from parameterized algorithms and structural graph theory will unify these fields and expand my professional network, significantly enhancing my career prospects.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences computer and information sciences internet
- natural sciences mathematics pure mathematics discrete mathematics graph theory
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2024-PF-01
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1165 KOBENHAVN
Denmark
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