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### Delineating imprecise regions via shortest-path graphs

Mark de Berg, Wouter Meulemans, Bettina Speckmann
2011 Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - GIS '11
We present a new method to delineate imprecise regions from a set of points that are likely to lie inside the region.  ...  We use shortest-path graphs based on the squared Euclidean distance which capture the shape of region boundaries well.  ...  In Section 4 we explain how to compute shortest-path graphs and how to turn them into a delineation for a vernacular regions.  ...

### Flow Computations on Imprecise Terrains [article]

Anne Driemel and Herman J. Haverkort and Maarten Löffler and Rodrigo Silveira
2012 arXiv   pre-print
We study the computation of the flow of water on imprecise terrains.  ...  In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x,y)-coordinates are fixed.  ...  Consider the graph G of the imprecise terrain. Let π be a path in G, with no repeated vertices.  ...

### Delineating Boundaries for Imprecise Regions [chapter]

Iris Reinbacher, Marc Benkert, Marc van Kreveld, Joseph S. B. Mitchell, Alexander Wolff
2005 Lecture Notes in Computer Science
region.  ...  In geographic information retrieval, queries often use names of geographic regions that do not have a well-defined boundary, such as "Southern France."  ...  The boundary of the polygon P * contains a path F * that connects v 1 and v 2 via b. The path F * consists of a shortest geodesic path between b and v 1 , and between b and v 2 .  ...

### Delineating Boundaries for Imprecise Regions

Iris Reinbacher, Marc Benkert, Marc van Kreveld, Joseph S. B. Mitchell, Jack Snoeyink, Alexander Wolff
2007 Algorithmica
region.  ...  In geographic information retrieval, queries often use names of geographic regions that do not have a well-defined boundary, such as "Southern France."  ...  The boundary of the polygon P * contains a path F * that connects v 1 and v 2 via b. The path F * consists of a shortest geodesic path between b and v 1 , and between b and v 2 .  ...

### Flow Computations on Imprecise Terrains [chapter]

Anne Driemel, Herman Haverkort, Maarten Löffler, Rodrigo I. Silveira
2011 Lecture Notes in Computer Science
We study water flow computation on imprecise terrains.  ...  In both cases each vertex has an imprecise elevation, given by an interval of possible values, while its (x, y)coordinates are fixed.  ...  Now we can easily make a decomposition of the graph into square regions of √ r 1 × √ r 1 nodes; we group these together into regions of √ r 2 × √ r 2 regions, etc., generally grouping regions of √ r i  ...

### Generating k-best solutions to auction winner determination problems

Terence Kelly, Andrew Byde
2006 ACM SIGecom Exchanges
Dynamic programs are longest-/shortest-paths problems [Ahuja et al. 1993]. 4. We can generate the k shortest paths in a graph [Eppstein 1998].  ...  We then compute k-shortest paths to generate k-best solutions to the WDP.  ...  are not generated when the k-shortest paths algorithm operates on the modified graph.  ...

### Complete removal of redundant expressions

Rastislav Bodík, Rajiv Gupta, Mary Lou Soffa
1998 SIGPLAN notices
The paper develops two methods for determining the optimization benefit of restructuring a program region, one based on path-profiles and the other on data-flow frequency analysis.  ...  In particular, using an elimination-style data-flow framework, we derive a demand-driven frequency analyzer whose cost can be controlled by permitting a bounded degree of conservative imprecision in the  ...  Figure 2 : 2 code motion prevented by CMP region b) CMP region diluted via code duplication c) complete PRE of [a+b] Removing obstacles to code motion via restructuring.  ...

### Complete removal of redundant expressions

Rastislav Bodík, Rajiv Gupta, Mary Lou Soffa
1998 Proceedings of the ACM SIGPLAN 1998 conference on Programming language design and implementation - PLDI '98
The paper develops two methods for determining the optimization benefit of restructuring a program region, one based on path-profiles and the other on data-flow frequency analysis.  ...  In particular, using an elimination-style data-flow framework, we derive a demand-driven frequency analyzer whose cost can be controlled by permitting a bounded degree of conservative imprecision in the  ...  Figure 2 : 2 code motion prevented by CMP region b) CMP region diluted via code duplication c) complete PRE of [a+b] Removing obstacles to code motion via restructuring.  ...

### Shortest-Path Constraints for 3D Multiobject Semiautomatic Segmentation Via Clustering and Graph Cut

Razmig Kechichian, Sebastien Valette, Michel Desvignes, Remy Prost
2013 IEEE Transactions on Image Processing
The shortest-path formulation produces a prior that is submodular which allows us to optimize (5) via the efficient Expansion Moves Graph Cut algorithm.  ...  Shortest-Path Constraints for 3D Multiobject Semiautomatic Segmentation via Clustering and Graph Cut Razmig Kéchichian, Sébastien Valette * , Michel Desvignes, and Rémy Prost, Member, IEEE Abstract-We  ...

### Gradients of connectivity distance are anchored in primary cortex

Sabine Oligschläger, Julia M. Huntenburg, Johannes Golchert, Mark E. Lauckner, Tyler Bonnen, Daniel S. Margulies
2016 Brain Structure and Function
Specifically, the further a region is located from primary sensorimotor regions, the more distant are its functional connections with other areas of the cortex.  ...  Connectivity between distant cortical areas is a valuable, yet costly feature of cortical organization and is predominantly found between regions of heteromodal association cortex.  ...  Notably, the shortest distances precisely delineated cortical landmarks of primary areas, bounding the lip of the calcarine sulcus that delineates the primary from the secondary visual cortex, the temporal  ...

### Algorithms for the Digital Restoration of Torn Films

D. Corrigan, A. Kokaram, N. Harte
2012 IEEE Transactions on Image Processing
This paper describes a method for delineating the tear boundary and for correcting the displacement.  ...  This is achieved using a graph-cut segmentation framework that can be either automatic or interactive when automatic segmentation is not possible.  ...  Instead of following the tear boundary, the segmentation boundary follows the shortest path to the perimeter of the frame.  ...

### Promoting Connectivity of Network-Like Structures by Enforcing Region Separation [article]

Doruk Oner and Mateusz Koziński and Leonardo Citraro and Nathan C. Dadap and Alexandra G. Konings and Pascal Fua
2020 arXiv   pre-print
It also prevents predicting false positive roads and canals by penalizing unwarranted disconnections of background regions.  ...  Our loss function is designed to prevent such unwanted connections between background regions, and therefore close the gaps in predicted roads.  ...  First, both roads and canals often form loops and even if a connection between two road pixels is missed, they may still be connected via a different path.  ...

### Nonlinearity and distance of ancient routes in the Aztec Empire

Igor Lugo, Martha G. Alatriste-Contreras, Dong Hoon Shin
2019 PLoS ONE
If a path length increases, so does its nonlinearity. Thus, the simple pattern of traveling in the Aztec region is fairly unlikely to be straight and short.  ...  This study explores the way in which traveling paths in ancient cultures are characterized by the relationship between nonlinear shapes and path lengths in terms of distances.  ...  a flat surface via straight-line routes.  ...

### Reconstructing tumor amplisomes

B. J. Raphael, P. A. Pevzner
2004 Bioinformatics
While many duplications associated with tumors have been identified (e.g. via techniques such as CGH), both the organization of the duplicated sequences and the process that leads to these duplications  ...  . , (v m , w m ) in H , find the shortest alternating path (cycle) A in H such that A contains an alternating path from v i to w i for each i = 1, . . . , m. Alternating Superpath Problem.  ...  In this case, we find the shortest alternating cycle that contains alternating paths for the largest number of pairs (v i , w i ).  ...

### Geo-Located Tweets. Enhancing Mobility Maps and Capturing Cross-Border Movement

Justine I. Blanford, Zhuojie Huang, Alexander Savelyev, Alan M. MacEachren, Renaud Lambiotte
2015 PLoS ONE
The findings from this study has broad implications for studying movement patterns and mapping inter/intra-region movement dynamics.  ...  We were also able to capture both long and short distances travelled, highlighting regional connections and cross-border movement between Kenya and the surrounding countries.  ...  It is calculated based on the length of the average shortest path between a vertex and all vertices in the graph: C C ðn i Þ ¼ X g j¼1 dðn i ; n j Þ " # À1 ð4Þ In which d(n i , n j ) is the distance between  ...
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