51 research outputs found
Taming Horizontal Instability in Merge Trees: On the Computation of a Comprehensive Deformation-based Edit Distance
Comparative analysis of scalar fields in scientific visualization often
involves distance functions on topological abstractions. This paper focuses on
the merge tree abstraction (representing the nesting of sub- or superlevel
sets) and proposes the application of the unconstrained deformation-based edit
distance. Previous approaches on merge trees often suffer from instability:
small perturbations in the data can lead to large distances of the
abstractions. While some existing methods can handle so-called vertical
instability, the unconstrained deformation-based edit distance addresses both
vertical and horizontal instabilities, also called saddle swaps. We establish
the computational complexity as NP-complete, and provide an integer linear
program formulation for computation. Experimental results on the TOSCA shape
matching ensemble provide evidence for the stability of the proposed distance.
We thereby showcase the potential of handling saddle swaps for comparison of
scalar fields through merge trees
On the complexity of Robust Stable Marriage
Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We focus on the complexity of finding an (a, b)-supermatch. An (a, b)-supermatch is defined as a stable matching in which if any a (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those a men/women and also the partners of at most b other couples. In order to show deciding if there exists an (a, b)-supermatch is NPNP -complete, we first introduce a SAT formulation that is NPNP -complete by using Schaefer’s Dichotomy Theorem. Then, we show the equivalence between the SAT formulation and finding a (1, 1)-supermatch on a specific family of instances
Listing Subgraphs by Cartesian Decomposition
We investigate a decomposition technique for listing problems in graphs and set systems. It is based on the Cartesian product of some iterators, which list the solutions of simpler problems. Our ideas applies to several problems, and we illustrate one of them in depth, namely, listing all minimum spanning trees of a weighted graph G. Here iterators over the spanning trees for unweighted graphs can be obtained by a suitable modification of the listing algorithm by [Shioura et al., SICOMP 1997], and the decomposition of G is obtained by suitably partitioning its edges according to their weights. By combining these iterators in a Cartesian product scheme that employs Gray coding, we give the first algorithm which lists all minimum spanning trees of G in constant delay, where the delay is the time elapsed between any two consecutive outputs. Our solution requires polynomial preprocessing time and uses polynomial space
The Perfect Matching Cut Problem Revisited
Under embargo until: 2022-09-20In a graph, a perfect matching cut is an edge cut that is a perfect matching. perfect matching cut (pmc) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP -complete. We revisit the problem and show that pmc remains NP -complete when restricted to bipartite graphs of maximum degree 3 and arbitrarily large girth. Complementing this hardness result, we give two graph classes in which pmc is polynomial time solvable. The first one includes claw-free graphs and graphs without an induced path on five vertices, the second one properly contains all chordal graphs. Assuming the Exponential Time Hypothesis, we show there is no O∗(2o(n)) -time algorithm for pmc even when restricted to n-vertex bipartite graphs, and also show that pmc can be solved in O∗(1.2721n) time by means of an exact branching algorithm.acceptedVersio
Shortest Route at Dynamic Location with Node Combination-Dijkstra Algorithm
Abstract— Online transportation has become a basic
requirement of the general public in support of all activities to go
to work, school or vacation to the sights. Public transportation
services compete to provide the best service so that consumers
feel comfortable using the services offered, so that all activities
are noticed, one of them is the search for the shortest route in
picking the buyer or delivering to the destination. Node
Combination method can minimize memory usage and this
methode is more optimal when compared to A* and Ant Colony
in the shortest route search like Dijkstra algorithm, but can’t
store the history node that has been passed. Therefore, using
node combination algorithm is very good in searching the
shortest distance is not the shortest route. This paper is
structured to modify the node combination algorithm to solve the
problem of finding the shortest route at the dynamic location
obtained from the transport fleet by displaying the nodes that
have the shortest distance and will be implemented in the
geographic information system in the form of map to facilitate
the use of the system.
Keywords— Shortest Path, Algorithm Dijkstra, Node
Combination, Dynamic Location (key words
The UNOR 40 plan (1971-1972) by Hestnes Ferreira: As a more structured expansion proposal for a planning unit in Lisbon
The aim of this paper is to present the work of Hestnes Ferreira and his team, namely for the UNOR 40 planning unit in Lisbon, as a study case of an infrastructural enhancement in Mainland Portugal during the early 1970s. The UNOR design teams were recruited outside the municipal staff. For UNOR40 the team was coordinated by Raúl Hestnes Ferreira and included architects Rodrigo Rau and Vicente Bravo, landscape architect Gonçalo Ribeiro Teles, and urban geographer, Jorge Gaspar. These oversaw the planning of a large area between Campo Grande and Benfica, using a traffic study developed by French consultants. The main results of the UNOR 40 Plan were to redefine the layout of the North-South Hub, Combatentes and LusÃada Avenues, as a way of ordering the urban network of this sector, including the urban access to Telheiras. The plan also comprised the creation of an institutional square, based on a program that included museums, institutes, office buildings, and a church. However, the applicability of the UNOR 40 Plan was practically nil, with the exception of the layout of some road links.info:eu-repo/semantics/publishedVersio
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