110,624 research outputs found
Space-Efficient DFS and Applications: Simpler, Leaner, Faster
The problem of space-efficient depth-first search (DFS) is reconsidered. A
particularly simple and fast algorithm is presented that, on a directed or
undirected input graph with vertices and edges, carries out a
DFS in time with bits of working memory, where is the
(total) degree of , for each , and . A slightly more complicated variant of the algorithm works in the same
time with at most bits. It is also shown that a DFS can
be carried out in a graph with vertices and edges in
time with bits or in time with either
bits or, for arbitrary integer , bits. These
results among them subsume or improve most earlier results on space-efficient
DFS. Some of the new time and space bounds are shown to extend to applications
of DFS such as the computation of cut vertices, bridges, biconnected components
and 2-edge-connected components in undirected graphs
Succinct Indexable Dictionaries with Applications to Encoding -ary Trees, Prefix Sums and Multisets
We consider the {\it indexable dictionary} problem, which consists of storing
a set for some integer , while supporting the
operations of \Rank(x), which returns the number of elements in that are
less than if , and -1 otherwise; and \Select(i) which returns
the -th smallest element in . We give a data structure that supports both
operations in O(1) time on the RAM model and requires bits to store a set of size , where {\cal B}(n,m) = \ceil{\lg
{m \choose n}} is the minimum number of bits required to store any -element
subset from a universe of size . Previous dictionaries taking this space
only supported (yes/no) membership queries in O(1) time. In the cell probe
model we can remove the additive term in the space bound,
answering a question raised by Fich and Miltersen, and Pagh.
We present extensions and applications of our indexable dictionary data
structure, including:
An information-theoretically optimal representation of a -ary cardinal
tree that supports standard operations in constant time,
A representation of a multiset of size from in bits that supports (appropriate generalizations of) \Rank
and \Select operations in constant time, and
A representation of a sequence of non-negative integers summing up to
in bits that supports prefix sum queries in constant
time.Comment: Final version of SODA 2002 paper; supersedes Leicester Tech report
2002/1
Gestão do patrimônio e identidade: centro de referência cultural e ecológica do engenho São João
O Engenho São João está localizado na Ilha de Itamaracá, no litoral do Estado de Pernambuco, Brasil. As primeiras fontes que fazem referência ao Engenho datam de 1747 e desde então ele é palco de importantes acontecimentos, como, por exemplo, o nascimento do Conselheiro João Alfredo em 1835, importante político abolicionista do período imperial brasileiro e a implantação da moenda a vapor, fazendo do local marco da modernização da indústria açucareira, precursor das usinas de açúcar no Brasil.
Em 1938, as terras do Engenho São João e todas as suas benfeitorias, mecanismos, matas e logradouros, são adquiridas pelo Estado, sendo aí instalada a Colônia Agrícola de Itamaracá, uma penitenciária em regime semi-aberto que funciona até os dias atuais (havendo atualmente uma decisão governamental de retirá-la até o ano de 2010). Em 1983, o engenho que contava com 2 edifícios referentes à época do engenho e 8 à época do funcionamento da Penitenciária, foi tombado pelo Estado. Em 1998, a Mata de São João, repleta de trilhas pitorescas, é reconhecida pela Unesco como Reserva da Biosfera da Mata Atlântica. Em 2007, após algumas intervenções de estabilização e recuperação das antigas edificações, o local passa a ser alvo de um projeto integrado, prevendo a preservação de sua paisagem cultural, através da implantação, em uma área de 20,83 ha, do Centro de Referência Cultural e Ecológica do Engenho São João. Nele deverão estar abrigados e preservados o ambiente natural, hábitos, fazeres, manualidades características locais e seus cenários de apresentação: presente e passado da Ilha e seus personagens consagrados. O presente artigo tem por objetivo empreender um debate em torno da interpretação, conservação e preservação dos edifícios do Engenho São João, tendo em vista a diversidade histórica e cultural que emana desse patrimônio, estabelecendo um fio condutor que evidencie a identidade do lugar.Tópico 1: Aspectos teóricos, históricos, legales, económicos y tecnológicos de la restauración y conservación de bienes patrimoniales
A delay analysis for opportunistic transmission in fading broadcast channels
We consider a single-antenna broadcast block fading channel (downlink scheduling) with n users where the transmission is packet-based and all users are backlogged. We define the delay as the minimum number of channel uses that guarantees all n users successfully receive m packets. This is a more stringent notion of delay than average delay and is the worst case delay among the users. A delay optimal scheduling scheme, such as round-robin, achieves the delay of mn. In a heterogeneous network and for the optimal throughput strategy where the transmitter sends the packet to the user with the best channel conditions, we derive the moment generating function of the delay for any m and n. For large n and in a homogeneous network, the expected delay in receiving one packet by all the receivers scales as n log n, as opposed to n for the round-robin scheduling. We also show that when m grows faster than (log n)^r, for some r > 1, then the expected value of delay scales like mn. This roughly determines the time-scale required for the system
to behave fairly in a homogeneous network. We then propose a
scheme to significantly reduce the delay at the expense of a small throughput hit.
We further look into two generalizations of our work: i) the
effect of temporal channel correlation and ii) the advantage of multiple transmit antennas on the delay. For a channel with memory of two, we prove that the delay scales again like n log n no matter how severe the correlation is. For a system with M transmit antennas, we prove that the expected delay in receiving one packet by all the users scales like (n log n)/(M +O((M^2)/n) for large n and when M is not growing faster than log n. Thus, when the temporal channel correlation is zero, multiple transmit antenna systems do not reduce the delay significantly. However, when channel correlation is present, they can lead to significant gains
by “decorrelating” the effective channel through means such as random beamforming
Succinct Color Searching in One Dimension
In this paper we study succinct data structures for one-dimensional color reporting and color counting problems.
We are given a set of n points with integer coordinates in the range [1,m] and every point is assigned a color from the set {1,...sigma}.
A color reporting query asks for the list of distinct colors that occur in a query interval [a,b] and a color counting query asks for the number of distinct colors in [a,b].
We describe a succinct data structure that answers approximate color counting queries in O(1) time and uses mathcal{B}(n,m) + O(n) + o(mathcal{B}(n,m)) bits,
where mathcal{B}(n,m) is the minimum number of bits required to represent an arbitrary set of size n from a universe of m elements. Thus we show, somewhat counterintuitively,
that it is not necessary to store colors of points in order to answer approximate color counting queries.
In the special case when points are in the rank space (i.e., when n=m), our data structure needs only O(n) bits.
Also, we show that Omega(n) bits are necessary in that case.
Then we turn to succinct data structures for color reporting.
We describe a data structure that uses mathcal{B}(n,m) + nH_d(S) + o(mathcal{B}(n,m)) + o(nlgsigma) bits and answers queries in O(k+1) time,
where k is the number of colors in the answer, and nH_d(S) (d=log_sigma n) is the d-th order empirical entropy of the color sequence. Finally, we consider succinct color reporting under restricted updates. Our dynamic data structure uses nH_d(S)+o(nlgsigma) bits and supports queries in O(k+1) time
More Haste, Less Waste: Lowering the Redundancy in Fully Indexable Dictionaries
We consider the problem of representing, in a compressed format, a bit-vector
of bits with 1s, supporting the following operations, where : returns the number of occurrences of bit in the
prefix ; returns the position of the th occurrence
of bit in . Such a data structure is called \emph{fully indexable
dictionary (FID)} [Raman et al.,2007], and is at least as powerful as
predecessor data structures. Our focus is on space-efficient FIDs on the
\textsc{ram} model with word size and constant time for all
operations, so that the time cost is independent of the input size. Given the
bitstring to be encoded, having length and containing ones, the
minimal amount of information that needs to be stored is . The state of the art in building a FID for is
given in [Patrascu,2008] using
bits, to support the operations in time. Here, we propose a parametric
data structure exhibiting a time/space trade-off such that, for any real
constants , it
uses B(n,m) + O(n^{1+\delta} + n (\frac{m}{n^s})^\eps) bits and performs
all the operations in time O(s\delta^{-1} + \eps^{-1}). The improvement is
twofold: our redundancy can be lowered parametrically and, fixing ,
we get a constant-time FID whose space is B(n,m) + O(m^\eps/\poly{n}) bits,
for sufficiently large . This is a significant improvement compared to the
previous bounds for the general case
Succinct Dynamic One-Dimensional Point Reporting
In this paper we present a succinct data structure for the dynamic one-dimensional range reporting problem. Given an interval [a,b] for some a,b in [m], the range reporting query on an integer set S subseteq [m] asks for all points in S cap [a,b]. We describe a data structure that answers reporting queries in optimal O(k+1) time, where k is the number of points in the answer, and supports updates in O(lg^epsilon m) expected time. Our data structure uses B(n,m) + o(B(n,m)) bits where B(n,m) is the minimum number of bits required to represent a set of size n from a universe of m elements. This is the first dynamic data structure for this problem that uses succinct space and achieves optimal query time
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