6,625 research outputs found
Parallelization of cycle-based logic simulation
Verification of digital circuits by Cycle-based simulation can be performed in parallel. The parallel implementation requires two phases: the compilation phase, that sets up the data needed for the
execution of the simulation, and the simulation phase, that consists in executing the parallel simulation of the considered circuit for a certain number of cycles. During the early phase of design, compilation phase has to be repeated each time a bug is found. Thus, if the time of the compilation phase is too high, the advantages stemming from the parallel approach may be lost. In this work we propose an
effective version of the compilation phase and compute the corresponding execution time. We also analyze the percentage of execution time required by the different steps of the compilation phase for
a set of literature benchmarks. Further, we implemented the simulation phase exploiting the GPU architecture, and we computed the execution times for a set of benchmarks obtaining values comparable
with literature ones. Finally, we implemented the sequential version of the Cycle-based simulation in such a way that the execution time is optimized. We used the sequential values to compute the speedup
of the parallel version for the considered set of benchmarks
On the complexity of optimal homotopies
In this article, we provide new structural results and algorithms for the
Homotopy Height problem. In broad terms, this problem quantifies how much a
curve on a surface needs to be stretched to sweep continuously between two
positions. More precisely, given two homotopic curves and
on a combinatorial (say, triangulated) surface, we investigate the problem of
computing a homotopy between and where the length of the
longest intermediate curve is minimized. Such optimal homotopies are relevant
for a wide range of purposes, from very theoretical questions in quantitative
homotopy theory to more practical applications such as similarity measures on
meshes and graph searching problems.
We prove that Homotopy Height is in the complexity class NP, and the
corresponding exponential algorithm is the best one known for this problem.
This result builds on a structural theorem on monotonicity of optimal
homotopies, which is proved in a companion paper. Then we show that this
problem encompasses the Homotopic Fr\'echet distance problem which we therefore
also establish to be in NP, answering a question which has previously been
considered in several different settings. We also provide an O(log
n)-approximation algorithm for Homotopy Height on surfaces by adapting an
earlier algorithm of Har-Peled, Nayyeri, Salvatipour and Sidiropoulos in the
planar setting
Long cycles, degree sums and neighborhood unions
AbstractFor a graph G, define the parameters α(G)=max{|S| |S is an independent set of vertices of G}, σk(G)=min{∑ki=1d(vi)|{v1,…,vk} is an independent set} and NCk(G)= min{|∪ki=1 N(vi)∥{v1,…,vk} is an independent set} (k⩾2). It is shown that every 1-tough graph G of order n⩾3 with σ3(G)⩾n+r⩾n has a cycle of length at least min{n,n+NCr+5+∈(n+r)(G)-α(G)}, where ε(i)=3(⌈13i⌉−13i). This result extends previous results in Bauer et al. (1989/90), Faßbender (1992) and Flandrin et al. (1991). It is also shown that a 1-tough graph G of order n⩾3 with σ3(G)⩾n+r⩾n has a cycle of length at least min{n,2NC⌊18(n+6r+17)⌋(G)}. Analogous results are established for 2-connected graphs
Persistent Homology Over Directed Acyclic Graphs
We define persistent homology groups over any set of spaces which have
inclusions defined so that the corresponding directed graph between the spaces
is acyclic, as well as along any subgraph of this directed graph. This method
simultaneously generalizes standard persistent homology, zigzag persistence and
multidimensional persistence to arbitrary directed acyclic graphs, and it also
allows the study of more general families of topological spaces or point-cloud
data. We give an algorithm to compute the persistent homology groups
simultaneously for all subgraphs which contain a single source and a single
sink in arithmetic operations, where is the number of vertices in
the graph. We then demonstrate as an application of these tools a method to
overlay two distinct filtrations of the same underlying space, which allows us
to detect the most significant barcodes using considerably fewer points than
standard persistence.Comment: Revised versio
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