2 Search Results for "Near, Joseph P."

Document
DOI: 10.4230/LIPIcs.SWAT.2020.7
Computing β-Stretch Paths in Drawings of Graphs

Authors: Esther M. Arkin, Faryad Darabi Sahneh, Alon Efrat, Fabian Frank, Radoslav Fulek, Stephen Kobourov, and Joseph S. B. Mitchell

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Let f be a drawing in the Euclidean plane of a graph G, which is understood to be a 1-dimensional simplicial complex. We assume that every edge of G is drawn by f as a curve of constant algebraic complexity, and the ratio of the length of the longest simple path to the the length of the shortest edge is poly(n). In the drawing f, a path P of G, or its image in the drawing π=f(P), is β-stretch if π is a simple (non-self-intersecting) curve, and for every pair of distinct points p∈P and q∈P, the length of the sub-curve of π connecting f(p) with f(q) is at most β||f(p)-f(q)‖, where ‖.‖ denotes the Euclidean distance. We introduce and study the β-stretch Path Problem (βSP for short), in which we are given a pair of vertices s and t of G, and we are to decide whether in the given drawing of G there exists a β-stretch path P connecting s and t. The βSP also asks that we output P if it exists. The βSP quantifies a notion of "near straightness" for paths in a graph G, motivated by gerrymandering regions in a map, where edges of G represent natural geographical/political boundaries that may be chosen to bound election districts. The notion of a β-stretch path naturally extends to cycles, and the extension gives a measure of how gerrymandered a district is. Furthermore, we show that the extension is closely related to several studied measures of local fatness of geometric shapes. We prove that βSP is strongly NP-complete. We complement this result by giving a quasi-polynomial time algorithm, that for a given ε>0, β∈O(poly(log |V(G)|)), and s,t∈V(G), outputs a β-stretch path between s and t, if a (1-ε)β-stretch path between s and t exists in the drawing.
Cite as

Esther M. Arkin, Faryad Darabi Sahneh, Alon Efrat, Fabian Frank, Radoslav Fulek, Stephen Kobourov, and Joseph S. B. Mitchell. Computing β-Stretch Paths in Drawings of Graphs. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 7:1-7:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arkin_et_al:LIPIcs.SWAT.2020.7,
  author =	{Arkin, Esther M. and Sahneh, Faryad Darabi and Efrat, Alon and Frank, Fabian and Fulek, Radoslav and Kobourov, Stephen and Mitchell, Joseph S. B.},
  title =	{{Computing \beta-Stretch Paths in Drawings of Graphs}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.7},
  URN =		{urn:nbn:de:0030-drops-122540},
  doi =		{10.4230/LIPIcs.SWAT.2020.7},
  annote =	{Keywords: stretch factor, dilation, geometric spanners}
}
Document
DOI: 10.4230/LIPIcs.ICLP.2010.144
From Relational Specifications to Logic Programs

Authors: Joseph P. Near

Published in: LIPIcs, Volume 7, Technical Communications of the 26th International Conference on Logic Programming (2010)

Abstract
This paper presents a compiler from expressive, relational specifications to logic programs. Specifically, the compiler translates the Imperative Alloy specification language to Prolog. Imperative Alloy is a declarative, relational specification language based on first-order logic and extended with imperative constructs; Alloy specifications are traditionally not executable. In spite of this theoretical limitation, the compiler produces useful prototype implementations for many specifications.
Cite as

Joseph P. Near. From Relational Specifications to Logic Programs. In Technical Communications of the 26th International Conference on Logic Programming. Leibniz International Proceedings in Informatics (LIPIcs), Volume 7, pp. 144-153, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

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@InProceedings{near:LIPIcs.ICLP.2010.144,
  author =	{Near, Joseph P.},
  title =	{{From Relational Specifications to Logic Programs}},
  booktitle =	{Technical Communications of the 26th International Conference on Logic Programming},
  pages =	{144--153},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-17-0},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{7},
  editor =	{Hermenegildo, Manuel and Schaub, Torsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2010.144},
  URN =		{urn:nbn:de:0030-drops-25924},
  doi =		{10.4230/LIPIcs.ICLP.2010.144},
  annote =	{Keywords: logic programming, specification languages, executable specifications}
}
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