Project description
Decomposing makes problems more digestible in the realm of graph theory
Graph theory has emerged as a very important area of discrete mathematics that uses a geometric approach to the study of objects, helping us to classify and represent data as a collection of edges or paths and vertices or nodes. It has found applications in numerous fields, from representing the interrelationships between objects on social media platforms to shortest path optimisations in GPS systems. The EU-funded BOBR project is focusing on pushing the boundaries of our understanding of decomposition methods in graph theory, breaking down large problems into smaller, more tractable ones with a focus on parametrised and approximation algorithms.
Objective
The main goal of the project is to radically expand our understanding of decomposition methods for discrete problems, with a particular focus on the design of parameterized and approximation algorithms on graphs. We will concentrate on four topics where we see a potential for either establishing new directions, or reaching far beyond the current state of the art.
(Beyond) Sparsity: The field of Sparsity is a rapidly developing area of graph theory that studies abstract notions of uniform sparseness in graphs and provides a wealth of tools for algorithm design. While there are still many unknowns within this field, we would like to reach beyond sparse graphs by developing a theory of well-structured dense graphs, inspired by the advances in Sparsity.
Parameterized dynamic algorithms: The idea of parameterization has so far received little attention in the field of dynamic algorithms. Our goal is to establish solid foundations for the direction of parameterized dynamic algorithms by providing dynamic variants of basic decomposition tools used in parameterized complexity.
Parameterization and approximation on planar graphs: The areas of parameterized algorithms and of approximation schemes on planar graphs share a core set of decomposition techniques and benefit from extensive cross-inspiration. We will approach several intriguing questions in this area while focusing on the idea of parameterized approximation schemes, where parameterization and approximation is explicitly combined.
Forbidding induced subgraphs: Structural graph theory offers a wealth of tools for understanding structure in graph classes characterized by forbidding induced subgraphs. This structure, while elusive and difficult to exploit, often leads to surprising tractability results. Motivated by recent advances, we propose to focus on finding general-use techniques for designing subexponential-time, approximation, and parameterized algorithms in this setting.
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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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
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.
ERC-STG - Starting Grant
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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) ERC-2020-STG
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00-927 WARSZAWA
Poland
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