51 research outputs found
Dissection with the Fewest Pieces is Hard, Even to Approximate
We prove that it is NP-hard to dissect one simple orthogonal polygon into another using a given number of pieces, as is approximating the fewest pieces to within a factor of 1+1/1080−ε .National Science Foundation (U.S.) (Grant CCF-1217423)National Science Foundation (U.S.) (Grant CCF-1065125)National Science Foundation (U.S.) (Grant CCF-1420692
A Time-Space Tradeoff for Triangulations of Points in the Plane
In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Approximation algorithms for maximally balanced connected graph partition
Given a simple connected graph , we seek to partition the vertex
set into non-empty parts such that the subgraph induced by each part is
connected, and the partition is maximally balanced in the way that the maximum
cardinality of these parts is minimized. We refer this problem to as {\em
min-max balanced connected graph partition} into parts and denote it as
{\sc -BGP}. The general vertex-weighted version of this problem on trees has
been studied since about four decades ago, which admits a linear time exact
algorithm; the vertex-weighted {\sc -BGP} and {\sc -BGP} admit a
-approximation and a -approximation, respectively; but no
approximability result exists for {\sc -BGP} when , except a
trivial -approximation. In this paper, we present another
-approximation for our cardinality {\sc -BGP} and then extend it to
become a -approximation for {\sc -BGP}, for any constant .
Furthermore, for {\sc -BGP}, we propose an improved -approximation.
To these purposes, we have designed several local improvement operations, which
could be useful for related graph partition problems.Comment: 23 pages, 7 figures, accepted for presentation at COCOA 2019 (Xiamen,
China
Malaria vector species in Colombia: a review
Here we present a comprehensive review of the literature on the vectorial importance of the major Anopheles malaria vectors in Colombia. We provide basic information on the geographical distribution, altitudinal range, immature habitats, adult behaviour, feeding preferences and anthropophily, endophily and infectivity rates. We additionally review information on the life cycle, longevity and population fluctuation of Colombian Anopheles species. Emphasis was placed on the primary vectors that have been epidemiologically incriminated in malaria transmission: Anopheles darlingi, Anopheles albimanus and Anopheles nuneztovari. The role of a selection of local, regional or secondary vectors (e.g., Anopheles pseudopunctipennis and Anopheles neivai) is also discussed. We highlight the importance of combining biological, morphological and molecular data for the correct taxonomical determination of a given species, particularly for members of the species complexes. We likewise emphasise the importance of studying the bionomics of primary and secondary vectors along with an examination of the local conditions affecting the transmission of malaria. The presence and spread of the major vectors and the emergence of secondary species capable of transmitting human Plasmodia are of great interest. When selecting control measures, the anopheline diversity in the region must be considered. Variation in macroclimate conditions over a species' geographical range must be well understood and targeted to plan effective control measures based on the population dynamics of the local Anopheles species
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