1,720,990 research outputs found
Testing Triangle Freeness in the General Model in Graphs with Arboricity O(√n)
Get PDFWe study the problem of testing triangle freeness in the general graph model. This problem was first studied in the general graph model by Alon et al. (SIAM J. Discret. Math. 2008) who provided both lower bounds and upper bounds that depend on the number of vertices and the average degree of the graph. Their bounds are tight only when d_max = O(d) and ̄{d} ≤ √n or when ̄{d} = Θ(1), where d_max denotes the maximum degree and ̄{d} denotes the average degree of the graph. In this paper we provide bounds that depend on the arboricity of the graph and the average degree. As in Alon et al., the parameters of our tester is the number of vertices, n, the number of edges, m, and the proximity parameter ε (the arboricity of the graph is not a parameter of the algorithm). The query complexity of our tester is Õ(Γ/ ̄{d} + Γ)⋅ poly(1/ε) on expectation, where Γ denotes the arboricity of the input graph (we use Õ(⋅) to suppress O(log log n) factors). We show that for graphs with arboricity O(√n) this upper bound is tight in the following sense. For any Γ ∈ [s] where s = Θ(√n) there exists a family of graphs with arboricity Γ and average degree ̄{d} such that Ω(Γ/ ̄{d} + Γ) queries are required for testing triangle freeness on this family of graphs. Moreover, this lower bound holds for any such Γ and for a large range of feasible average degrees
A Centralized Local Algorithm for the Sparse Spanning Graph Problem
Get PDFConstructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries.
Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most (1+epsilon)n edges (where n is the number of vertices and epsilon is a given approximation/sparsity parameter). We achieve a query complexity of O~(poly(Delta/epsilon)n^{2/3}), where Delta is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary bounded degree graphs. Moreover, we achieve the additional property that our algorithm outputs a spanning subgraph of bounded stretch i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of O(log n * (Delta+log n)/epsilon) hops in the output that connects its endpoints
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Testing Hamiltonicity (And Other Problems) in Minor-Free Graphs
Get PDFIn this paper we provide sub-linear algorithms for several fundamental problems in the setting in which the input graph excludes a fixed minor, i.e., is a minor-free graph. In particular, we provide the following algorithms for minor-free unbounded degree graphs.
1) A tester for Hamiltonicity with two-sided error with poly(1/ε)-query complexity, where ε is the proximity parameter.
2) A local algorithm, as defined by Rubinfeld et al. (ICS 2011), for constructing a spanning subgraph with almost minimum weight, specifically, at most a factor (1+ε) of the optimum, with poly(1/ε)-query complexity. Both our algorithms use partition oracles, a tool introduced by Hassidim et al. (FOCS 2009), which are oracles that provide access to a partition of the graph such that the number of cut-edges is small and each part of the partition is small. The polynomial dependence in 1/ε of our algorithms is achieved by combining the recent poly(d/ε)-query partition oracle of Kumar-Seshadhri-Stolman (ECCC 2021) for minor-free graphs with degree bounded by d.
For bounded degree minor-free graphs we introduce the notion of covering partition oracles which is a relaxed version of partition oracles and design a poly(d/ε)-time covering partition oracle for this family of graphs. Using our covering partition oracle we provide the same results as above (except that the tester for Hamiltonicity has one-sided error) for minor-free bounded degree graphs, as well as showing that any property which is monotone and additive (e.g. bipartiteness) can be tested in minor-free graphs by making poly(d/ε)-queries.
The benefit of using the covering partition oracle rather than the partition oracle in our algorithms is its simplicity and an improved polynomial dependence in 1/ε in the obtained query complexity
Brief Announcement: A Centralized Local Algorithm for the Sparse Spanning Graph Problem
Get PDFConstructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries.
Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most (1+epsilon)n edges (where n is the number of vertices and epsilon is a given approximation/sparsity parameter). We achieve a query complexity of O(poly(Delta/epsilon)n^(2/3)) (up to polylogarithmic factors in n) where Delta is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary bounded degree graphs. Moreover, we achieve the additional property that our algorithm outputs a spanner, i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of O(log n (Delta+log n)/epsilon) hops in the output that connects its endpoints
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Distributed Testing of Graph Isomorphism in the CONGEST Model
Get PDFIn this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, G_U, is isomorphic to G_K which is given as an input to all the nodes in the network, or alternatively, only to a single node.
We first consider the decision variant of the problem in which the algorithm should distinguish the case where G_U and G_K are isomorphic from the case where G_U and G_K are not isomorphic. Specifically, if G_U and G_K are not isomorphic then w.h.p. at least one node should output reject and otherwise all nodes should output accept . We provide a randomized algorithm with O(n) rounds for the setting in which G_K is given only to a single node. We prove that for this setting the number of rounds of any deterministic algorithm is Ω̃(n²) rounds, where n denotes the number of nodes, which implies a separation between the randomized and the deterministic complexities of deciding GI . Our algorithm can be adapted to the semi-streaming model, where a single pass is performed and Õ(n) bits of space are used.
We then consider the property testing variant of the problem, where the algorithm is only required to distinguish the case that G_U and G_K are isomorphic from the case that G_U and G_K are far from being isomorphic (according to some predetermined distance measure). We show that every (possibly randomized) algorithm, requires Ω(D) rounds, where D denotes the diameter of the network. This lower bound holds even if all the nodes are given G_K as an input, and even if the message size is unbounded. We provide a randomized algorithm with an almost matching round complexity of O(D+(ε^{-1}log n)²) rounds that is suitable for dense graphs (namely, graphs with Ω(n²) edges).
We also show that with the same number of rounds it is possible that each node outputs its mapping according to a bijection which is an approximate isomorphism.
We conclude with simple simulation arguments that allow us to adapt centralized property testing algorithms and obtain essentially tight algorithms with round complexity Õ(D) for special families of sparse graphs
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Local Algorithms for Sparse Spanning Graphs
Get PDFWe initiate the study of the problem of designing sublinear-time (local) algorithms that, given an edge (u,v) in a connected graph G=(V,E), decide whether (u,v) belongs to a sparse spanning graph G' = (V,E') of G. Namely, G' should be connected and |E'| should be upper bounded by (1+epsilon)|V| for a given parameter epsilon > 0. To this end the algorithms may query the incidence relation of the graph G, and we seek algorithms whose query complexity and running time (per given edge (u,v)) is as small as possible. Such an algorithm may be randomized but (for a fixed choice of its random coins) its decision on different edges in the graph should be consistent with the same spanning graph G' and independent of the order of queries.
We first show that for general (bounded-degree) graphs, the query complexity of any such algorithm must be Omega(sqrt{|V|}). This lower bound holds for graphs that have high expansion. We then turn to design and analyze algorithms both for graphs with high expansion (obtaining a result that roughly matches the lower bound) and for graphs that are (strongly) non-expanding (obtaining results in which the complexity does not depend on |V|). The complexity of the problem for graphs that do not fall into these two categories is left as an open question
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