Objective
"Many problems we face are naturally expressed in terms of distances. Rather than solving each one on an ad hoc basis, researchers have built a rich toolbox. Metric embeddings play a central role: points of a complex metric space are embedded into a simpler one (e.g. a tree metric or Euclidean space) while approximately preserving structure. This lets us solve the problem in the simple space—where fast, well-understood algorithms exist—and then transfer solutions back. Metric embeddings have enabled breakthroughs for many different problems. However, many real networks are not metric. Problems with non-metric distances are considerably harder, and our current toolkit is quite limited. The overarching goal of this proposal is to develop a toolkit for non-metric distance problems and apply it to advance multiple core tasks.
The guiding idea of embeddings is to impose more ""structure"" on the input space. Completely general distances are notoriously intractable, so we target non-metrics that have some structure:
(1) Quasimetrics — shortest-path distances in directed graphs (lacking symmetry). We will develop tools such as stochastic embeddings into DAGs, locality-sensitive partial orderings, and directed low-diameter decompositions, with special focus on realistic instances that have additional structure (e.g. small highway dimension). Expected impact includes faster directed shortest paths, improved sparsest-cut approximations, compact routing, asymmetric TSP, and beyond.
(2) Hop-constrained (h.c.) distances — the u–v distance is the minimum-weight path using at most h hops. H.c. distances are important for increased reliability and lower latency. We will study stochastic embeddings into trees, embeddings into spanning trees, and embeddings of topologically structured graphs into low-treewidth graphs. Expected impact includes better (non-h.c.) oblivious routing, distributed universal optimality, h.c. compact routing, and more."
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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.1.1 - 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
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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-ERC - HORIZON ERC Grants
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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-2026-STG
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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.
52900 Ramat Gan
Israel
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.