"The activities, in project scheduling, can be represented graphically in two different ways, by either assigning the activities to the nodes 'AoN' directed acyclic graph (dag) or to the arcs 'AoA dag'. In this paper, a new algorithm is proposed for generating, for a given project scheduling problem, an Activity-on-Arc dag starting from the Activity-on-Node dag using the concepts of line graphs of graphs."

"We proposed two new exact algorithms to detect network motifs of size 3 and 4. Considering that motifs need to count the isomorphic patterns in the original graph $G(V,E)$ and in a set of randomized graphs, the following complexities concern about count isomorphic patterns in a single graph. Let $m=|E|$ and let $a(G)$ be the arboricity of $G$. Assume $|E|geq|V|$. We describe a $O(a(G)m)$ time complexity algorithm to count isomorphic patterns of size 3. The complexity is a $O({msqrt{m}})$ in the worst graph. The second algorithm is a $O(m^2)$ complexity algorithm to count isomorphic patterns of size 4. The final result was expressive faster when compared with other implemented algorithms."

"This paper presents a study on two data structures that have been used to model several problems in computer science: and/or graphs and x-y graphs. An and/or graph is an acyclic digraph containing a source, such that every vertex v has a label f(v) in {and,or} and edges represent dependency relations between vertices: a vertex labeled and depends on all of its out-neighbors, while a vertex labeled or depends on only one of its out-neighbors. X-y graphs are defined as a natural generalization of and/or graphs: every vertex vi of an x-y graph has a label xi-yi to mean that vi depends on xi of its yi out-neighbors. We analyze the complexity of the optimization problems Min-and/or and Min-x-y, which consist of finding solution subgraphs of optimal weight for and/or and x-y graphs, respectively. Motivated by the large applicability as well as the hardness of Min-and/or and Min-x-y, we study new complexity aspects of such problems, both from a classical and a parameterized point of view. …"

"In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if and only if they coincide on a node at the same time. We conduct numerical study on the consensus problem in this framework and show that global consensus can be achieved."

"In this paper we define what we call an affinity system, which is a set of individuals, each with a vector characterizing its preference for all other individuals in the set. The preference of a member can be given either by a ranking of all members or by a weighted vector that defines the degrees of its affinity to others. Affinity systems are useful for modeling social systems as well as general data sets, as social interactions are often determined by affinities among the members. We also define a natural notion of (potentially overlapping) communities in an affinity system, in which the members of a given community collectively prefer each other to anyone else outside the community. Thus these communities are "self-determined" or "self-certified" by the affinity system. We provide a tight polynomial bound on the number of self-determined communities as a function of the robustness of the community. Moreover, we present a polynomial-time algorithm for enumerating these communities, as well as a local algorithm with a strong stochastic performance guarantee that can find a community in time nearly linear in the of size the community.…"

"In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel algorithm for the problem which can be run on every parallel machine."

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number, the Thue chromatic number, the harmonious chromatic number and the clique chromatic number of $P_4$-tidy graphs and $(q,q-4)$-graphs, for every fixed $q$. These classes include cographs, $P_4$-sparse and $P_4$-lite graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter $q(G)$, which is the minimum $q$ such that $G$ is a $(q,q-4)$-graph. We also prove that every connected $(q,q-4)$-graph with at least $q$ vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive.

Matching dependencies (MDs) have been recently introduced as declarative rules for entity resolution (ER), i.e. for identifying and resolving duplicates in relational instance $D$. A set of MDs can be used as the basis for a possibly non-deterministic mechanism that computes a duplicate-free instance from $D$. The possible results of this process are the clean, "minimally resolved instances" (MRIs). There might be several MRIs for $D$, and the "resolved answers" to a query are those that are shared by all the MRIs. We investigate the problem of computing resolved answers. We look at various sets of MDs, developing syntactic criteria for determining (in)tractability of the resolved answer problem, including a dichotomy result. For some tractable classes of MDs and conjunctive queries, we present a query rewriting methodology that can be used to retrieve the resolved answers. We also investigate connections with "consistent query answering", deriving further tractability results for MD-based ER.

"The k-domination number of a graph is the minimum size of a set X such that every vertex of G is in distance at most k from X. We give a linear time constant-factor approximation algorithm for k-domination number in classes of graphs with bounded expansion, which include e.g. proper minor-closed graph classes, classes closed on topological minors or classes of graphs that can be drawn on a fixed surface with bounded number of crossings on each edge.

The algorithm is based on the following approximate min-max characterization. A subset A of vertices of a graph G is d-independent if the distance between each pair of vertices in A is greater than d. Note that the size of the largest 2k-independent set is a lower bound for the k-domination number. We show that every graph from a fixed class with bounded expansion contains a 2k-independent set A and a k-dominating set D such that |D|=O(|A|), and these sets can be found in linear time. For domination number (k=1) the assumptions can be relaxed, and the result holds for all graph classes with arrangeability bounded by a constant."

"In the Partial Vertex Cover (PVC) problem we are given an undirected graph G = (V, E), a positive cost associated with each vertex and a positive integer k and the goal is to find a minimum cost subset of vertices S such that atleast k edges of the graph are covered. In this paper we consider two new generalization of the PVC problem. In the first variation which we call Partition Vertex Cover (Partition-VC) problem, the edges of the graph G are divided into n disjoint partitions $P_1, P_2... P_n$ and we have to select a minimum cost subset of vertices S such that atleast $k_i$ edges are covered from partition $P_i$. In the second variation which we call Knapsack Partition Vertex Cover (KPVC) problem, in addition to the previous conditions, each edge e has a profit $pi_{e}$ associated with it and we have an added knapsack constraint that the total profit of the covered edges in partition $P_i$ should be atleast $Pi_i$. We give an $O(log n)$ approximation for both the problems using a combination of deterministic rounding and randomized rounding approach that operates on the LP strengthened by adding Knapsack Cover inequalities as proposed by Carr, Fleischer, Leung & Phillips. We also show that these bounds can not be further improved by reducing the set cover problem to the Partition-VC problem in polynomial time. We also give an $O(f)$ approximation for the Partition-VC problem using a primal dual schema where f is the maximum number of edges in any partition."

"Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set $P$, respectively. First, we construct in $O(nlog{n})$ time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in $O(nlog n)$ time a 2-edge connected geometric planar graph spanning $P$ with max edge length bounded by $sqrt{5}$ times the optimal, assuming that the set $P$ forms a connected Unit Disk Graph. Second, we prove that 2 times the optimal is always sufficient if the set of points forms a 2 edge connected Unit Disk Graph and give an algorithm that runs in $O(n^2)$ time. We also show that for $k in O(sqrt{n})$, there exists a set $P$ of $n$ points in the plane such that even though the Unit Disk Graph spanning $P$ is $k$-vertex connected, there is no 2-edge connected geometric planar graph spanning $P$ even if the length of its edges is allowed to be up to 17/16."

"We present a $(1+epsilon)$-approximation algorithm running in $O(f(epsilon)cdot n log^2 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths."

"Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} in F. Given G and F, the path avoiding forbidden pairs (PAFP) problem is to find a safe s-t path in G. We systematically study the complexity of different special cases of the PAFP problem defined according to the mutual positions of fobidden pairs. Fix one topological ordering of vertices; we say that pairs {u, v} and {x, y} are disjoint, if u, v < x, y, nested, if u < x, y < v, and halving, if u < x < v < y. The PAFP problem is known to be NP-hard in general or if no two pairs are disjoint; we prove that it remains NP-hard even when no two forbidden pairs are nested. On the other hand, if no two pairs are halving, the problem is known to be solvable in cubic time. We simplify and improve this result by showing an O(M(n)) time algorithm, where M(n) is the time to multiply two n times n boolean matrices."

"We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. For example, in Walshaw's well known benchmark tables we are able to improve or recompute 76% of entries for the tables with 1%, 3% and 5% imbalance."

"Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not have the same color. In this research report, we focus on wireless sensor networks with grid topologies. How does a coloring algorithm take advantage of the regularity of grid topology to provide an optimal periodic coloring, that is a coloring with the minimum number of colors? We propose the Vector-Based Coloring Method, denoted VCM, a new method that is able to provide an optimal periodic coloring for any radio transmission range and for any h-hop coloring, h>=1. This method consists in determining at which grid nodes a color can be reproduced without creating interferences between these nodes while minimizing the number of colors used. We compare the number of colors provided by VCM with the number of colors obtained by a distributed coloring algorithm with line and column priority assignments. We also provide bounds on the number of colors of optimal general colorings of the infinite grid, and show that periodic colorings (and thus VCM) are asymptotically optimal. Finally, we discuss the applicability of this method to a real wireless network."

"We have developed a framework to study the struc- ture and function of complex networks in purely geomet- ric terms. In this framework, two common properties of complex network topologies, strong heterogeneity and clustering, turn out to be simple reflections of the basic properties of an underlying hyperbolic geometry. Heterogeneity, measured in terms of the power-law degree distribution exponent, is a function of the negative curvature of the hyperbolic space, while clustering reflects its metric property."

"We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal."

"The study of evolution of networks has received increased interest with the recent discovery that many real-world networks possess many things in common, in particular the manner of evolution of such networks. By adding a dimension of time to graph analysis, evolving graphs present opportunities and challenges to extract valuable information. This paper introduces the Evolving Graph Markup Language (EGML), an XML application for representing evolving graphs and related results. Along with EGML, a software tool is provided for the study of evolving graphs. New evolving graph drawing techniques based on the force-directed graph layout algorithm are also explored. Our evolving graph techniques reduce vertex movements between graph instances, so that an evolving graph can be viewed with smooth transitions"

"We propose a novel distributed algorithm to cluster graphs. The algorithm recovers the solution obtained from spectral clustering without the need for expensive eigenvalue/vector computations. We prove that, by propagating waves through the graph, a local fast Fourier transform yields the local component of every eigenvector of the Laplacian matrix, which are used to cluster graphs. For large graphs, the proposed algorithm is orders of magnitude faster than random walk based approaches. We prove the equivalence of the proposed algorithm to spectral clustering and derive convergence rates. We also demonstrate the benefit of using this decentralized clustering algorithm to accelerate distributed estimation for sensor networks and for efficient computation of distributed multi-agent search strategies."

I wonder to what extent this sort of thing might be useful in heuristics for Pareto-ranking

"Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general branching strategy that branches on the forbidden subgraphs of a relaxed class of graphs. By using the class of P4-sparse graphs as the relaxed graph class, we obtain efficient bounded-search tree algorithms for several parameterized deletion problems. For the cograph edge-deletion problem and the trivially perfect edge-deletion problem, the branching strategy yields the first non-trivial bounded-search tree algorithms. For the cograph vertex deletion problem, the running time of our simple bounded search algorithm matches those previously designed with the help of complicated case distinctions and non-trivial running time analysis [16] and computer-aided branching rules [7]"

"Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even trivial. A natural step, outstanding thus far, was to provide a broad classification of graphs that make for polynomial or NP-complete instances. We provide such a classification based on the set of allowed vertex degrees in the input graphs, yielding a full dichotomy on the complexity of the problem. As byproducts, the previous NP-completeness result for binary trees was strengthened to strictly binary trees, and the three-dimensional version of the problem was for the first time proven to be NP-complete. Our results were made possible by introducing the concepts of consistent orientations and robust gadgets, and by showing how the former allows NP-completeness proofs by local replacement even in the absence of the latter."

"The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the {\em randomness} of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called {\em configuration model}. In this paper we analyze four methods of DAG randomization as defined by the desired combination of topological invariants (directed and undirected degree sequence and component distributions) aimed to be preserved.…"

"We believe that our result could shed the light on the relation between the distribution of motifs and the struc- ture of the adjacency matrix of a hierarchical network. However to make this relation more profound the “in- verse” problem should be considered as well. Namely, it would be desirable to check if the stable distribution of motifs is uniquely related to any kind of hierarchical organization of the network."

"We describe a variation of a technique by Chiba and Nishizeki [3], leading to a data structure for graph algorithmic problems, called the h-graph data structure. It supports operations of insertion and removal of vertices, as well as insertion and removal of edges. Although the data structure can be used for general purpose, it is particularly suitable for applications in dynamic graph algorithms."

"The underlying reality of a succession of interbreeding populations is a vastly complicated network N. Since Darwin, species trees have been used as a simplified description of the relationships which summarize the overly complicated network N. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are situations where trees are inadequate. Consequently it is important to determine properties that characterize networks closely related to N and possibly more complicated than trees but lacking the full complexity of N."

"A recent study by researchers in Yale and published in PNAS shows that there are significant differences between the network topologies of living systems like E. coli and complex pieces of software such as the Linux Operating System."

"… The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for random topologies."

"Scholars have long asserted that social structure is an important feature of a variety of societal institutions. As part of a larger effort to develop a fully integrated model of judicial decision making, we argue that social structure-operationalized as the professional and social connections between judicial actors-partially directs outcomes in the hierarchical federal judiciary. Since different social structures impose dissimilar consequences upon outputs, the precursor to evaluating the doctrinal consequences that a given social structure imposes is a descriptive effort to characterize its properties. Given the difficulty associated with obtaining appropriate data for federal judges, it is necessary to rely upon a proxy measure to paint a picture of the social landscape. In the aggregate, we believe the flow of law clerks reflects a reasonable proxy for social and professional linkages between jurists...."

Interesting prospect for a Nudge application