Dominating Set
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Combinatorial Landscape Analysis for Dominating Set and Vertex Coloring
arXiv:2606.07361v1 Announce Type: new Abstract: We analyze the two combinatorial problems of Dominating Set and Vertex Coloring regarding what kind of local optima are present for various instances. For a variety of graph classes each, we determine whether the induced landscapes are unimodal, plateau-unimodal (all optima are just one plateau), equimodal (all local optima are global) or truly multimodal. We do this for two different neighborhood operators, one based on making only a single...
Benchmarking the ORCA PT-2 Boson Sampler using Minimum Dominating Set Problems
Announce Type: cross Abstract: We use boson sampling as part of a gradient-free variational algorithm (the Binary Bosonic Solver) to solve a minimum dominating set problem and compare these results to a number of exact and heuristic classical algorithms. The boson sampling has been performed on the physical PT-2 time-bin interferometer from ORCA Computing. The PT-2 device has been tested here using both a single- and double-loop configuration and the results are compared based on the best...
Benchmarking the ORCA PT-2 Boson Sampler using Minimum Dominating Set Problems
arXiv:2605.30935v2 Announce Type: replace-cross Abstract: We use boson sampling as part of a gradient-free variational algorithm (the Binary Bosonic Solver) to solve a minimum dominating set problem and compare these results to a number of exact and heuristic classical algorithms. The boson sampling has been performed on the physical PT-2 time-bin interferometer from ORCA Computing. The PT-2 device has been tested here using both a single- and double-loop configuration and the results are...
Minimum Complete MR Subsets under Semantic-Mutation Fault Models: A Support-Set Domination Boundary
arXiv:2606.08269v1 Announce Type: new Abstract: This paper asks when MR-subset selection is a real mutant-level requirement for minimum complete evidence in metamorphic testing rather than a coarse fault-class counting artifact. We define a layer-relative completeness criterion over an admitted mutant--draw coverage universe. The central result is a support-set domination boundary: it states when class-level abstraction is safe and when mutant-level MR minimization is necessary.
Constrained Dominant Sets for Multimodal Document Question Answering
arXiv:2606.07252v1 Announce Type: new Abstract: Long multimodal document question answering is limited by which evidence reaches the reader, rather than by the quantity retrieved. In lengthy documents, findings often recur across figures, captions, and introductory sentences, causing similarity based retrievers in modern multimodal retrieval-augmented generation (RAG) systems to allocate resources to near-duplicates while overlooking complementary evidence. This work introduces a retriever...
Constrained Dominant Sets for Multimodal Document Question Answering
Announce Type: replace Abstract: Long multimodal document question answering is limited by which evidence reaches the reader, rather than by the quantity retrieved. In lengthy documents, findings often recur across figures, captions, and introductory sentences, causing similarity based retrievers in modern multimodal retrieval-augmented generation (RAG) systems to allocate resources to near-duplicates while overlooking complementary evidence. This work introduces a retriever that selects...
Southern energy corridors set to dominate supplies to Europe, global leaders say
The rapid reshape of global energy supply routes and markets is a key focus at the Baku Energy Week 2026. Opening Baku Energy Week 2026, Azerbaijan’s President Ilham Aliyev said the “world cannot live without fossil fuels,” while also insisting that countries “should be judged on how they invest in renewables.” Speaking about Azerbaijan’s role in global energy markets, Aliyev said it was “difficult to imagine what the European market would look like without the South Caucasus,” underscoring...
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Massive Blue Origin rocket explosion sets stage for Elon Musk’s dominance of space
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Hamilton fastest as Ferrari dominate Monaco practice
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