Matches in SemOpenAlex for { <https://semopenalex.org/work/W2530757973> ?p ?o ?g. }
Showing items 1 to 94 of
94
with 100 items per page.
- W2530757973 abstract "In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. They were introduced by the author in complexity classification of minimum 0-extension problems. We clarify the relationship to other discrete convex functions, such as $k$-submodular functions, skew-bisubmodular functions, L$^natural$-convex functions, tree submodular functions, and UJ-convex functions. We show that they are actually viewed as submodular/L-convex functions in our sense. We also prove a sharp iteration bound of the steepest descent algorithm for minimizing our L-convex functions. The underlying structures, modular semilattices and oriented modular graphs, have rich connections to projective and polar spaces, Euclidean building, and metric spaces of global nonpositive curvature (CAT(0) spaces). By utilizing these connections, we formulate an analogue of the Lov'asz extension, introduce well-behaved subclasses of submodular/L-convex functions, and show that these classes can be characterized by the convexity of the Lov'asz extension. We demonstrate applications of our theory to combinatorial optimization problems that include multicommodity flow, multiway cut, and related labeling problems: these problems have been outside the scope of discrete convex analysis so far." @default.
- W2530757973 created "2016-10-21" @default.
- W2530757973 creator A5090989020 @default.
- W2530757973 date "2016-10-07" @default.
- W2530757973 modified "2023-10-16" @default.
- W2530757973 title "L-convexity on graph structures" @default.
- W2530757973 cites W1498671329 @default.
- W2530757973 cites W1507799342 @default.
- W2530757973 cites W1568640725 @default.
- W2530757973 cites W1706395838 @default.
- W2530757973 cites W1780622159 @default.
- W2530757973 cites W1877564947 @default.
- W2530757973 cites W1908692903 @default.
- W2530757973 cites W1930126570 @default.
- W2530757973 cites W1962311560 @default.
- W2530757973 cites W1973005928 @default.
- W2530757973 cites W1979962887 @default.
- W2530757973 cites W1983075526 @default.
- W2530757973 cites W1983818015 @default.
- W2530757973 cites W2010004564 @default.
- W2530757973 cites W2022245976 @default.
- W2530757973 cites W2028404519 @default.
- W2530757973 cites W2046344295 @default.
- W2530757973 cites W2049688189 @default.
- W2530757973 cites W2053552665 @default.
- W2530757973 cites W2073337839 @default.
- W2530757973 cites W2091898665 @default.
- W2530757973 cites W2094731111 @default.
- W2530757973 cites W2098047723 @default.
- W2530757973 cites W2160614591 @default.
- W2530757973 cites W2304678994 @default.
- W2530757973 cites W2407339229 @default.
- W2530757973 cites W2480301421 @default.
- W2530757973 cites W2570081448 @default.
- W2530757973 cites W3105827122 @default.
- W2530757973 cites W50901504 @default.
- W2530757973 doi "https://doi.org/10.48550/arxiv.1610.02469" @default.
- W2530757973 hasPublicationYear "2016" @default.
- W2530757973 type Work @default.
- W2530757973 sameAs 2530757973 @default.
- W2530757973 citedByCount "4" @default.
- W2530757973 countsByYear W25307579732016 @default.
- W2530757973 countsByYear W25307579732017 @default.
- W2530757973 countsByYear W25307579732018 @default.
- W2530757973 crossrefType "posted-content" @default.
- W2530757973 hasAuthorship W2530757973A5090989020 @default.
- W2530757973 hasBestOaLocation W25307579731 @default.
- W2530757973 hasConcept C101468663 @default.
- W2530757973 hasConcept C106159729 @default.
- W2530757973 hasConcept C111919701 @default.
- W2530757973 hasConcept C112680207 @default.
- W2530757973 hasConcept C114614502 @default.
- W2530757973 hasConcept C118615104 @default.
- W2530757973 hasConcept C12108790 @default.
- W2530757973 hasConcept C126255220 @default.
- W2530757973 hasConcept C157972887 @default.
- W2530757973 hasConcept C162324750 @default.
- W2530757973 hasConcept C178621042 @default.
- W2530757973 hasConcept C2524010 @default.
- W2530757973 hasConcept C33923547 @default.
- W2530757973 hasConcept C41008148 @default.
- W2530757973 hasConcept C72134830 @default.
- W2530757973 hasConceptScore W2530757973C101468663 @default.
- W2530757973 hasConceptScore W2530757973C106159729 @default.
- W2530757973 hasConceptScore W2530757973C111919701 @default.
- W2530757973 hasConceptScore W2530757973C112680207 @default.
- W2530757973 hasConceptScore W2530757973C114614502 @default.
- W2530757973 hasConceptScore W2530757973C118615104 @default.
- W2530757973 hasConceptScore W2530757973C12108790 @default.
- W2530757973 hasConceptScore W2530757973C126255220 @default.
- W2530757973 hasConceptScore W2530757973C157972887 @default.
- W2530757973 hasConceptScore W2530757973C162324750 @default.
- W2530757973 hasConceptScore W2530757973C178621042 @default.
- W2530757973 hasConceptScore W2530757973C2524010 @default.
- W2530757973 hasConceptScore W2530757973C33923547 @default.
- W2530757973 hasConceptScore W2530757973C41008148 @default.
- W2530757973 hasConceptScore W2530757973C72134830 @default.
- W2530757973 hasLocation W25307579731 @default.
- W2530757973 hasOpenAccess W2530757973 @default.
- W2530757973 hasPrimaryLocation W25307579731 @default.
- W2530757973 hasRelatedWork W2144899307 @default.
- W2530757973 hasRelatedWork W2175532135 @default.
- W2530757973 hasRelatedWork W2394104306 @default.
- W2530757973 hasRelatedWork W2983049021 @default.
- W2530757973 hasRelatedWork W3003165794 @default.
- W2530757973 hasRelatedWork W4243129259 @default.
- W2530757973 hasRelatedWork W4287899549 @default.
- W2530757973 hasRelatedWork W4297899479 @default.
- W2530757973 hasRelatedWork W4312910031 @default.
- W2530757973 hasRelatedWork W4378552409 @default.
- W2530757973 isParatext "false" @default.
- W2530757973 isRetracted "false" @default.
- W2530757973 magId "2530757973" @default.
- W2530757973 workType "article" @default.