Development of a data model to facilitate rapid Watershed Delineation

Scott Haag; Ali Shokoufandeh

Home/Archive/arXiv

arXiv · 1611.09131

Development of a data model to facilitate rapid Watershed Delineation

Scott Haag·Ali Shokoufandeh

View original source ↗Read source document ↗Export metadata ↓

Abstract

A data model to store and retrieve surface watershed boundaries using graph theoretic approaches is proposed. This data model integrates output from a standard digital elevation models (DEM) derived stream catchment boundaries, and vector representation of stream centerlines then applies them to three novel algorithms. The first is called Modified Nested Set (MNS), which is a depth first graph traversal algorithm that searches across stream reaches (vertices) and stream junctions (edges) labeling vertices by their discovery time, finish time, and distance from the root. The second is called Log Reduced Graphs (LRG), which creates a set S of logarithmically reduced graphs from the original data, to store the watershed boundaries. The final algorithm is called Stitching Watershed, which provides a technique to merge watershed boundaries across the set of graphs created in the LRG algorithm. This technique was applied to the ~ 30,600 km2 Delaware River Watershed and compared to hypothetical data storage models in terms of prep-processing, data storage, and query complexity costs. Results show that the proposed technique provides significant benefits vs. the hypothetical methods with a 99-98% reduction in prepossessing, 96-80% reduction in query complexity and a 76% reduction in storage costs. The increasing availability of high resolution elevation data within the United States and the internationally provides an opportunity to extend these results to other watersheds through the world.

Explore related subjects

cs.DS cs.CE

Keep this discovery

BibTeX RIS

Scott Haag, Ali Shokoufandeh. 2016-11-11. Development of a data model to facilitate rapid Watershed Delineation. https://arxiv.org/abs/1611.09131

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗