2,189 research outputs found
Parametric shortest-path algorithms via tropical geometry
We study parameterized versions of classical algorithms for computing
shortest-path trees. This is most easily expressed in terms of tropical
geometry. Applications include shortest paths in traffic networks with variable
link travel times.Comment: 24 pages and 8 figure
An Output-sensitive Algorithm for Computing Projections of Resultant Polytopes
We develop an incremental algorithm to compute the Newton polytope
of the resultant, aka resultant polytope, or its
projection along a given direction.
The resultant is fundamental in algebraic elimination and
in implicitization of parametric hypersurfaces.
Our algorithm exactly computes vertex- and halfspace-representations
of the desired polytope using an oracle producing resultant vertices in a
given direction.
It is output-sensitive as it uses one oracle call per vertex.
We overcome the bottleneck of determinantal predicates
by hashing, thus accelerating execution from to times.
We implement our algorithm using the experimental CGAL package {\tt
triangulation}.
A variant of the algorithm computes successively tighter inner and outer
approximations: when these polytopes have, respectively,
90\% and 105\% of the true volume, runtime is reduced up to times.
Our method computes instances of -, - or -dimensional polytopes
with K, K or vertices, resp., within hr.
Compared to tropical geometry software, ours is faster up to
dimension or , and competitive in higher dimensions
Statistical mechanics of two-dimensional foams: Physical foundations of the model
In a recent series of papers [1--3], a statistical model that accounts for
correlations between topological and geometrical properties of a
two-dimensional shuffled foam has been proposed and compared with experimental
and numerical data. Here, the various assumptions on which the model is based
are exposed and justified: the equiprobability hypothesis of the foam
configurations is argued. The range of correlations between bubbles is
discussed, and the mean field approximation that is used in the model is
detailed. The two self-consistency equations associated with this mean field
description can be interpreted as the conservation laws of number of sides and
bubble curvature, respectively. Finally, the use of a '' Grand-Canonical ''
description, in which the foam constitutes a reservoir of sides and curvature,
is justified
Identifying combinations of tetrahedra into hexahedra: a vertex based strategy
Indirect hex-dominant meshing methods rely on the detection of adjacent
tetrahedra an algorithm that performs this identification and builds the set of
all possible combinations of tetrahedral elements of an input mesh T into
hexahedra, prisms, or pyramids. All identified cells are valid for engineering
analysis. First, all combinations of eight/six/five vertices whose connectivity
in T matches the connectivity of a hexahedron/prism/pyramid are computed. The
subset of tetrahedra of T triangulating each potential cell is then determined.
Quality checks allow to early discard poor quality cells and to dramatically
improve the efficiency of the method. Each potential hexahedron/prism/pyramid
is computed only once. Around 3 millions potential hexahedra are computed in 10
seconds on a laptop. We finally demonstrate that the set of potential hexes
built by our algorithm is significantly larger than those built using
predefined patterns of subdivision of a hexahedron in tetrahedral elements.Comment: Preprint submitted to CAD (26th IMR special issue
Synthesis of all-digital delay lines
© 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe synthesis of delay lines (DLs) is a core task during the generation of matched delays, ring oscillator clocks or delay monitors. The main figure of merit of a DL is the fidelity to track variability. Unfortunately, complex systems have a great diversity of timing paths that exhibit different sensitivities to static and dynamic variations. Designing DLs that capture this diversity is an ardous task. This paper proposes an algorithmic approach for the synthesis of DLs that can be integrated in a conventional design flow. The algorithm uses heuristics to perform a combinatorial search in a vast space of solutions that combine different types of gates and wire lengths. The synthesized DLs are (1) all digital, i.e., built of conventional standard cells, (2) accurate in tracking variability and (3) configurable at runtime. Experimental results with a commercial standard cell library confirm the quality of the DLs that only exhibit delay mismatches of about 1% on average over all PVT corners.Peer ReviewedPostprint (author's final draft
- …