Matches in SemOpenAlex for { <https://semopenalex.org/work/W1511409012> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W1511409012 abstract "We study the problem of finding shortest non-crossing thick paths in a polygonal domain, where a thick is the Minkowski sum of a usual (zero-thickness, or thin) and a disk. Given K pairs of terminals on the boundary of a simple n-gon, we compute in O(n + K) time a representation of the set of K shortest non-crossing thick paths joining the terminal pairs; using the representation, any particular can be output in time proportional to its complexity. In a polygonal domain with h holes we compute K shortest thick non-crossing paths in O (( K + 1)hh! poly(n,K)) time, using an efficient method to compute any one of the K thick paths if the threadings of all paths amidst the holes are specified. We show that if h is not constant, the problem is NP-hard; we also show the hardness of approximation. We give a pseudopolynomial-time algorithm for some rectilinear versions of the problem. We apply our thick paths algorithms to obtain the first algorithmic results for the minimum-cost flow problem—an extension of the standard discrete minimum-cost network flow problem to domains. The results are based on showing a analog of the Network Flow Decomposition Theorem. We investigate the problem of finding the maximum number of thick paths that can be routed in a polygonal domain. Using a modification of the continuous uppermost path algorithm, we give a constructive proof of a Menger-type result: the maximum number of paths equals to the length of a shortest in the thresholded critical graph of the domain. The algorithm computes (a representation of) the paths in O( nh + n log n) time. We show how to use the algorithm to find maximum monotone flows and paths. For simple polygons we give faster, linear-time algorithms. The non-crossing thick paths problems, as well as the flow problems, arise in the air traffic management problem of optimally routing air traffic lanes in Flow Constrained Areas while avoiding weather hazards, no-fly zones, and other constraints. The other motivations for studying the problems come from wire routing for circuits and from information propagation in sensor networks. We also consider other motion planning problems: the touring problems, shortest paths with bounded number of links in rectilinear domains, and optimal tours in pixelated environments and grids." @default.
- W1511409012 created "2016-06-24" @default.
- W1511409012 creator A5001506153 @default.
- W1511409012 date "2007-01-01" @default.
- W1511409012 modified "2023-09-26" @default.
- W1511409012 title "Thick non-crossing paths and minimum-cost continuous flows in polygonal domains" @default.
- W1511409012 hasPublicationYear "2007" @default.
- W1511409012 type Work @default.
- W1511409012 sameAs 1511409012 @default.
- W1511409012 citedByCount "3" @default.
- W1511409012 countsByYear W15114090122019 @default.
- W1511409012 crossrefType "dissertation" @default.
- W1511409012 hasAuthorship W1511409012A5001506153 @default.
- W1511409012 hasConcept C112680207 @default.
- W1511409012 hasConcept C11413529 @default.
- W1511409012 hasConcept C114614502 @default.
- W1511409012 hasConcept C118615104 @default.
- W1511409012 hasConcept C132525143 @default.
- W1511409012 hasConcept C134306372 @default.
- W1511409012 hasConcept C157469704 @default.
- W1511409012 hasConcept C173870130 @default.
- W1511409012 hasConcept C17744445 @default.
- W1511409012 hasConcept C182860218 @default.
- W1511409012 hasConcept C199360897 @default.
- W1511409012 hasConcept C199539241 @default.
- W1511409012 hasConcept C22590252 @default.
- W1511409012 hasConcept C2524010 @default.
- W1511409012 hasConcept C2776359362 @default.
- W1511409012 hasConcept C2777735758 @default.
- W1511409012 hasConcept C33923547 @default.
- W1511409012 hasConcept C36503486 @default.
- W1511409012 hasConcept C38349280 @default.
- W1511409012 hasConcept C41008148 @default.
- W1511409012 hasConcept C62354387 @default.
- W1511409012 hasConcept C79464548 @default.
- W1511409012 hasConcept C94625758 @default.
- W1511409012 hasConceptScore W1511409012C112680207 @default.
- W1511409012 hasConceptScore W1511409012C11413529 @default.
- W1511409012 hasConceptScore W1511409012C114614502 @default.
- W1511409012 hasConceptScore W1511409012C118615104 @default.
- W1511409012 hasConceptScore W1511409012C132525143 @default.
- W1511409012 hasConceptScore W1511409012C134306372 @default.
- W1511409012 hasConceptScore W1511409012C157469704 @default.
- W1511409012 hasConceptScore W1511409012C173870130 @default.
- W1511409012 hasConceptScore W1511409012C17744445 @default.
- W1511409012 hasConceptScore W1511409012C182860218 @default.
- W1511409012 hasConceptScore W1511409012C199360897 @default.
- W1511409012 hasConceptScore W1511409012C199539241 @default.
- W1511409012 hasConceptScore W1511409012C22590252 @default.
- W1511409012 hasConceptScore W1511409012C2524010 @default.
- W1511409012 hasConceptScore W1511409012C2776359362 @default.
- W1511409012 hasConceptScore W1511409012C2777735758 @default.
- W1511409012 hasConceptScore W1511409012C33923547 @default.
- W1511409012 hasConceptScore W1511409012C36503486 @default.
- W1511409012 hasConceptScore W1511409012C38349280 @default.
- W1511409012 hasConceptScore W1511409012C41008148 @default.
- W1511409012 hasConceptScore W1511409012C62354387 @default.
- W1511409012 hasConceptScore W1511409012C79464548 @default.
- W1511409012 hasConceptScore W1511409012C94625758 @default.
- W1511409012 hasLocation W15114090121 @default.
- W1511409012 hasOpenAccess W1511409012 @default.
- W1511409012 hasPrimaryLocation W15114090121 @default.
- W1511409012 hasRelatedWork W1535869571 @default.
- W1511409012 hasRelatedWork W1561670232 @default.
- W1511409012 hasRelatedWork W1606833362 @default.
- W1511409012 hasRelatedWork W1975595599 @default.
- W1511409012 hasRelatedWork W1980484820 @default.
- W1511409012 hasRelatedWork W2009056209 @default.
- W1511409012 hasRelatedWork W2022670034 @default.
- W1511409012 hasRelatedWork W2036921250 @default.
- W1511409012 hasRelatedWork W2047629658 @default.
- W1511409012 hasRelatedWork W2077159475 @default.
- W1511409012 hasRelatedWork W2092529578 @default.
- W1511409012 hasRelatedWork W2115001291 @default.
- W1511409012 hasRelatedWork W2131651363 @default.
- W1511409012 hasRelatedWork W2159148319 @default.
- W1511409012 hasRelatedWork W2212293515 @default.
- W1511409012 hasRelatedWork W2221579990 @default.
- W1511409012 hasRelatedWork W2493762868 @default.
- W1511409012 hasRelatedWork W2810759650 @default.
- W1511409012 hasRelatedWork W2950856291 @default.
- W1511409012 hasRelatedWork W3047272818 @default.
- W1511409012 isParatext "false" @default.
- W1511409012 isRetracted "false" @default.
- W1511409012 magId "1511409012" @default.
- W1511409012 workType "dissertation" @default.