102 research outputs found
Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs
Recently we presented the first algorithm for maintaining the set of nodes
reachable from a source node in a directed graph that is modified by edge
deletions with total update time, where is the number of edges and
is the number of nodes in the graph [Henzinger et al. STOC 2014]. The
algorithm is a combination of several different algorithms, each for a
different vs. trade-off. For the case of the
running time is , just barely below . In
this paper we simplify the previous algorithm using new algorithmic ideas and
achieve an improved running time of . This gives,
e.g., for the notorious case . We obtain the
same upper bounds for the problem of maintaining the strongly connected
components of a directed graph undergoing edge deletions. Our algorithms are
correct with high probabililty against an oblivious adversary.Comment: This paper was presented at the International Colloquium on Automata,
Languages and Programming (ICALP) 2015. A full version combining the findings
of this paper and its predecessor [Henzinger et al. STOC 2014] is available
at arXiv:1504.0795
The value of location in keyword auctions
Sponsored links on search engines are an emerging advertising tool, whereby a number of slots are put on sale through keyword auctions. This is also known as contextual advertising. Slot assignment and pricing in keyword auctions are then essential for the search engine\u2019s management since provide the main stream of revenues, and are typically accomplished by the Generalized Second Price (GSP) mechanism. In GSP the price of slots is a monotone function of the slot location, being larger for the highest slots. Though a higher location is associated with larger revenues, the lower costs associated with the lowest slots may make them more attractive for the advertiser. The contribution of this research is to show, by analytical and simulation results based on the theory of order statistics, that advertisers may not get the optimal slot they aim at (the slot maximizing their expected profit) and that the GSP mechanism may be unfair to all the winning bidders but the one who submitted the lowest bid
2-Vertex Connectivity in Directed Graphs
We complement our study of 2-connectivity in directed graphs, by considering
the computation of the following 2-vertex-connectivity relations: We say that
two vertices v and w are 2-vertex-connected if there are two internally
vertex-disjoint paths from v to w and two internally vertex-disjoint paths from
w to v. We also say that v and w are vertex-resilient if the removal of any
vertex different from v and w leaves v and w in the same strongly connected
component. We show how to compute the above relations in linear time so that we
can report in constant time if two vertices are 2-vertex-connected or if they
are vertex-resilient. We also show how to compute in linear time a sparse
certificate for these relations, i.e., a subgraph of the input graph that has
O(n) edges and maintains the same 2-vertex-connectivity and vertex-resilience
relations as the input graph, where n is the number of vertices.Comment: arXiv admin note: substantial text overlap with arXiv:1407.304
IMPLEMENTASI BUDAYA LITERASI DALAM PEMBENTUKAN KARAKTER INTEGRITAS SISWA DI SMA NEGERI 02 BATU
This study aims to describes the implementation of literacy culture in reporting the integrity character of students at SMA Negeri 02 Batu; mistakes and the solution of the problem in implementing literacy culture in order to characterize the integrity of students at SMA Negeri 02 Batu.
The research method used qualitative research and descriptive approaches. This research consists of procedures, implementation and data analysis. The data technique are uses observation, interview and documentation. The data analysis technique consist of four stages of activity, namely data collection, data reduction, data presentation, and drawing conclusions. The data validity technique used source triangulation.
The results showed that the implementation of Cultural Literacy was carried out through various stages, namely the habituation, development and learning stages. Constraints originating from GLS administrators and teachers are those who lack literacy training, students are low reading interest and different character of students, family is an understanding of the understanding of the character of education at home. Damage to GLS administrators and teachers, the solution is to provide training to improve competence, to students the solution is to motivate and approach each student, trust that comes from parents, the solution provides an understanding of character education at home
Effective Edge-Fault-Tolerant Single-Source Spanners via Best (or Good) Swap Edges
Computing \emph{all best swap edges} (ABSE) of a spanning tree of a given
-vertex and -edge undirected and weighted graph means to select, for
each edge of , a corresponding non-tree edge , in such a way that the
tree obtained by replacing with enjoys some optimality criterion (which
is naturally defined according to some objective function originally addressed
by ). Solving efficiently an ABSE problem is by now a classic algorithmic
issue, since it conveys a very successful way of coping with a (transient)
\emph{edge failure} in tree-based communication networks: just replace the
failing edge with its respective swap edge, so as that the connectivity is
promptly reestablished by minimizing the rerouting and set-up costs. In this
paper, we solve the ABSE problem for the case in which is a
\emph{single-source shortest-path tree} of , and our two selected swap
criteria aim to minimize either the \emph{maximum} or the \emph{average
stretch} in the swap tree of all the paths emanating from the source. Having
these criteria in mind, the obtained structures can then be reviewed as
\emph{edge-fault-tolerant single-source spanners}. For them, we propose two
efficient algorithms running in and time, respectively, and we show that the guaranteed (either
maximum or average, respectively) stretch factor is equal to 3, and this is
tight. Moreover, for the maximum stretch, we also propose an almost linear time algorithm computing a set of \emph{good} swap edges,
each of which will guarantee a relative approximation factor on the maximum
stretch of (tight) as opposed to that provided by the corresponding BSE.
Surprisingly, no previous results were known for these two very natural swap
problems.Comment: 15 pages, 4 figures, SIROCCO 201
Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time
We present faster algorithms for computing the 2-edge and 2-vertex strongly
connected components of a directed graph, which are straightforward
generalizations of strongly connected components. While in undirected graphs
the 2-edge and 2-vertex connected components can be found in linear time, in
directed graphs only rather simple -time algorithms were known. We use
a hierarchical sparsification technique to obtain algorithms that run in time
. For 2-edge strongly connected components our algorithm gives the
first running time improvement in 20 years. Additionally we present an -time algorithm for 2-edge strongly connected components, and thus
improve over the running time also when . Our approach
extends to k-edge and k-vertex strongly connected components for any constant k
with a running time of for edges and for vertices
Stability of oligosaccharides derived from lactulose during the processing of milk and apple juice
The scientific evidence on the bioactivity of oligosaccharides from lactulose has encouraged us to study their physicochemical modifications during the processing of milk and apple juice. The carbohydrate fraction with a degree of polymerization ≥3 was stable in milk heated at temperatures up to 100°C for 30 min and in apple juice heated up to 90°C for 15 min. An assessment of the Maillard reaction in heated milk pointed out a higher formation of furosine in milk with oligosaccharides from lactulose as compared to its counterpart without this ingredient, due to a higher presence of galactose. The organoleptic properties of juice with oligosaccharides from lactulose were acceptable and similar to those of apple juice with commercial galactooligosaccharides. The results presented herein demonstrate that oligosaccharides from lactulose can be used as prebiotic ingredients in a wide range of functional foods, including those intended for diabetics and lactose intolerant individuals.This work has been supported by project AGL2011-27884 from Spanish Ministerio de Economía y Competitividad.Peer Reviewe
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