5,502 research outputs found

    Incremental 22-Edge-Connectivity in Directed Graphs

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    In this paper, we initiate the study of the dynamic maintenance of 22-edge-connectivity relationships in directed graphs. We present an algorithm that can update the 22-edge-connected blocks of a directed graph with nn vertices through a sequence of mm edge insertions in a total of O(mn)O(mn) time. After each insertion, we can answer the following queries in asymptotically optimal time: (i) Test in constant time if two query vertices vv and ww are 22-edge-connected. Moreover, if vv and ww are not 22-edge-connected, we can produce in constant time a "witness" of this property, by exhibiting an edge that is contained in all paths from vv to ww or in all paths from ww to vv. (ii) Report in O(n)O(n) time all the 22-edge-connected blocks of GG. To the best of our knowledge, this is the first dynamic algorithm for 22-connectivity problems on directed graphs, and it matches the best known bounds for simpler problems, such as incremental transitive closure.Comment: Full version of paper presented at ICALP 201

    Strong Connectivity in Directed Graphs under Failures, with Application

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    In this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let GG be a digraph with mm edges and nn vertices, and let GeG\setminus e be the digraph obtained after deleting edge ee from GG. As a first result, we show how to compute in O(m+n)O(m+n) worst-case time: (i)(i) The total number of strongly connected components in GeG\setminus e, for all edges ee in GG. (ii)(ii) The size of the largest and of the smallest strongly connected components in GeG\setminus e, for all edges ee in GG. Let GG be strongly connected. We say that edge ee separates two vertices xx and yy, if xx and yy are no longer strongly connected in GeG\setminus e. As a second set of results, we show how to build in O(m+n)O(m+n) time O(n)O(n)-space data structures that can answer in optimal time the following basic connectivity queries on digraphs: (i)(i) Report in O(n)O(n) worst-case time all the strongly connected components of GeG\setminus e, for a query edge ee. (ii)(ii) Test whether an edge separates two query vertices in O(1)O(1) worst-case time. (iii)(iii) Report all edges that separate two query vertices in optimal worst-case time, i.e., in time O(k)O(k), where kk is the number of separating edges. (For k=0k=0, the time is O(1)O(1)). All of the above results extend to vertex failures. All our bounds are tight and are obtained with a common algorithmic framework, based on a novel compact representation of the decompositions induced by the 11-connectivity (i.e., 11-edge and 11-vertex) cuts in digraphs, which might be of independent interest. With the help of our data structures we can design efficient algorithms for several other connectivity problems on digraphs and we can also obtain in linear time a strongly connected spanning subgraph of GG with O(n)O(n) edges that maintains the 11-connectivity cuts of GG and the decompositions induced by those cuts.Comment: An extended abstract of this work appeared in the SODA 201

    Approximating the Smallest Spanning Subgraph for 2-Edge-Connectivity in Directed Graphs

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    Let GG be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of GG that maintains respectively: the 22-edge-connected blocks of GG (\textsf{2EC-B}); the 22-edge-connected components of GG (\textsf{2EC-C}); both the 22-edge-connected blocks and the 22-edge-connected components of GG (\textsf{2EC-B-C}). All three problems are NP-hard, and thus we are interested in efficient approximation algorithms. For \textsf{2EC-C} we can obtain a 3/23/2-approximation by combining previously known results. For \textsf{2EC-B} and \textsf{2EC-B-C}, we present new 44-approximation algorithms that run in linear time. We also propose various heuristics to improve the size of the computed subgraphs in practice, and conduct a thorough experimental study to assess their merits in practical scenarios

    Decremental Single-Source Reachability in Planar Digraphs

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    In this paper we show a new algorithm for the decremental single-source reachability problem in directed planar graphs. It processes any sequence of edge deletions in O(nlog2nloglogn)O(n\log^2{n}\log\log{n}) total time and explicitly maintains the set of vertices reachable from a fixed source vertex. Hence, if all edges are eventually deleted, the amortized time of processing each edge deletion is only O(log2nloglogn)O(\log^2 n \log \log n), which improves upon a previously known O(n)O(\sqrt{n}) solution. We also show an algorithm for decremental maintenance of strongly connected components in directed planar graphs with the same total update time. These results constitute the first almost optimal (up to polylogarithmic factors) algorithms for both problems. To the best of our knowledge, these are the first dynamic algorithms with polylogarithmic update times on general directed planar graphs for non-trivial reachability-type problems, for which only polynomial bounds are known in general graphs

    What’s In It For Me? Why Narcissists Help Others

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    Grandiose and vulnerable narcissists are both self-absorbed and highly entitled, yet they can also exhibit prosocial behavior, helping others under some circumstances. We predict that grandiose and vulnerable narcissists differ in their motivations to help, and these motivations may be influenced by their interpersonal goals and the perceived status of the target they wish to help. First, participants completed self-report measures assessing their levels of grandiose narcissism, vulnerable narcissism, and their interpersonal goals. Next, they completed a behavioral measure of helpfulness, where participants could help a fictitious partner complete a tangram task. We manipulated the status of their partner so participants perceived a low-status partner (high school student), an equal-status partner (same year in college), or a high-status partner (a graduate student). Results show that both narcissistic subtypes help when put in a situation where helping is normative but reported different helping motivations and experiences. For example, after helping, grandiose narcissists felt superior, special, respected, and like a hero –these effects were sometimes amplified when participants were also high in self-image goals or were helping a low-status individual. In comparison, vulnerable narcissists were less likely to help low-status individuals and reported motivations to help such as appearing likable, not being judged by the partner, and not being judged by the researcher. These results suggest grandiose and vulnerable narcissists may use helping as a way to boost their ego but in different ways (e.g. either for self-enhancement or social approval).  No embargoAcademic Major: Psycholog

    Dynamic Algorithms for the Massively Parallel Computation Model

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    The Massive Parallel Computing (MPC) model gained popularity during the last decade and it is now seen as the standard model for processing large scale data. One significant shortcoming of the model is that it assumes to work on static datasets while, in practice, real-world datasets evolve continuously. To overcome this issue, in this paper we initiate the study of dynamic algorithms in the MPC model. We first discuss the main requirements for a dynamic parallel model and we show how to adapt the classic MPC model to capture them. Then we analyze the connection between classic dynamic algorithms and dynamic algorithms in the MPC model. Finally, we provide new efficient dynamic MPC algorithms for a variety of fundamental graph problems, including connectivity, minimum spanning tree and matching.Comment: Accepted to the 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2019
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