DDSL: Efficient Subgraph Listing on Distributed and Dynamic Graphs

Subgraph listing is a fundamental problem in graph theory and has wide applications in areas like sociology, chemistry, and social networks. Modern graphs can usually be large-scale as well as highly dynamic, which challenges the efficiency of existing subgraph listing algorithms. Recent works have shown the benefits of partitioning and processing big graphs in a distributed system, however, there is only few work targets subgraph listing on dynamic graphs in a distributed environment. In this paper, we propose an efficient approach, called Distributed and Dynamic Subgraph Listing (DDSL), which can incrementally update the results instead of running from scratch. DDSL follows a general distributed join framework. In this framework, we use a Neighbor-Preserved storage for data graphs, which takes bounded extra space and supports dynamic updating. After that, we propose a comprehensive cost model to estimate the I/O cost of listing subgraphs. Then based on this cost model, we develop an algorithm to find the optimal join tree for a given pattern. To handle dynamic graphs, we propose an efficient left-deep join algorithm to incrementally update the join results. Extensive experiments are conducted on real-world datasets. The results show that DDSL outperforms existing methods in dealing with both static dynamic graphs in terms of the responding time

On hamiltonian colorings of block graphs

A hamiltonian coloring c of a graph G of order p is an assignment of colors to the vertices of G such that $D(u,v)+|c(u)-c(v)|\geq p-1$ for every two distinct vertices u and v of G, where D(u,v) denoted the detour distance between u and v. The value hc(c) of a hamiltonian coloring c is the maximum color assigned to a vertex of G. The hamiltonian chromatic number, denoted by hc(G), is the min{hc(c)} taken over all hamiltonian coloring c of G. In this paper, we present a lower bound for the hamiltonian chromatic number of block graphs and give a sufficient condition to achieve the lower bound. We characterize symmetric block graphs achieving this lower bound. We present two algorithms for optimal hamiltonian coloring of symmetric block graphs.Comment: 12 pages, 1 figure. A conference version appeared in the proceedings of WALCOM 201

On local structures of cubicity 2 graphs

A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the $X$-axis, distance $1 + \epsilon$ ($0 < \epsilon < 1$) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation

Common adversaries form alliances: modelling complex networks via anti-transitivity

Anti-transitivity captures the notion that enemies of enemies are friends, and arises naturally in the study of adversaries in social networks and in the study of conflicting nation states or organizations. We present a simplified, evolutionary model for anti-transitivity influencing link formation in complex networks, and analyze the model's network dynamics. The Iterated Local Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step, and joins anti-clones to the parent node's non-neighbor set. The graphs generated by ILAT exhibit familiar properties of complex networks such as densification, short distances (bounded by absolute constants), and bad spectral expansion. We determine the cop and domination number for graphs generated by ILAT, and finish with an analysis of their clustering coefficients. We interpret these results within the context of real-world complex networks and present open problems

Parameterized lower bound and NP-completeness of some HH-free Edge Deletion problems

For a graph $H$, the $H$-free Edge Deletion problem asks whether there exist at most $k$ edges whose deletion from the input graph $G$ results in a graph without any induced copy of $H$. We prove that $H$-free Edge Deletion is NP-complete if $H$ is a graph with at least two edges and $H$ has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-complete problems cannot be solved in parameterized subexponential time, i.e., in time $2^{o(k)}\cdot |G|^{O(1)}$, unless Exponential Time Hypothesis fails.Comment: 15 pages, COCOA 15 accepted pape

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

Cortical Neurons Develop Insulin Resistance and Blunted Akt Signaling: A Potential Mechanism Contributing to Enhanced Ischemic Injury in Diabetes

Patients with diabetes are at higher risk of stroke and experience increased morbidity and mortality after stroke. We hypothesized that cortical neurons develop insulin resistance, which decreases neuroprotection via circulating insulin and insulin-like growth factor-I (IGF-I). Acute insulin treatment of primary embryonic cortical neurons activated insulin signaling including phosphorylation of the insulin receptor, extracellular signal-regulated kinase (ERK), Akt, p70S6K, and glycogen synthase kinase-3- (GSK-3-). To mimic insulin resistance, cortical neurons were chronically treated with 25-mM glucose, 0.2-mM palmitic acid (PA), or 20-nM insulin before acute exposure to 20-nM insulin. Cortical neurons pretreated with insulin, but not glucose or PA, exhibited blunted phosphorylation of Akt, p70S6K, and GSK-3- with no change detected in ERK. Inhibition of the phosphatidylinositol 3-kinase (PI3-K) pathway during insulin pretreatment restored acute insulin-mediated Akt phosphorylation. Cortical neurons in adult BKS-db/db mice exhibited higher basal Akt phosphorylation than BKS-db+ mice and did not respond to insulin. Our results indicate that prolonged hyperinsulinemia leads to insulin resistance in cortical neurons. Decreased sensitivity to neuroprotective ligands may explain the increased neuronal damage reported in both experimental models of diabetes and diabetic patients after ischemia-reperfusion injury. Antioxid. Redox Signal. 14, 1829-1839.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90430/1/ars-2E2010-2E3816.pd

Heterokairy: a significant form of developmental plasticity?

There is a current surge of research interest in the potential role of developmental plasticity in adaptation and evolution. Here we make a case that some of this research effort should explore the adaptive significance of heterokairy, a specific type of plasticity that describes environmentally driven, altered timing of development within a species. This emphasis seems warranted given the pervasive occurrence of heterochrony, altered developmental timing between species, in evolution. We briefly review studies investigating heterochrony within an adaptive context across animal taxa, including examples that explore links between heterokairy and heterochrony. We then outline how sequence heterokairy could be included within the research agenda for developmental plasticity. We suggest that the study of heterokairy may be particularly pertinent in (i) determining the importance of non-adaptive plasticity, and (ii) embedding concepts from comparative embryology such as developmental modularity and disassociation within a developmental plasticity framework

Local Thermometry of Neutral Modes on the Quantum Hall Edge

A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.Comment: 24 pages, 18 figure

Reducing the clique and chromatic number via edge contractions and vertex deletions.

We consider the following problem: can a certain graph parameter of some given graph G be reduced by at least d, for some integer d, via at most k graph operations from some specified set S, for some given integer k? As graph parameters we take the chromatic number and the clique number. We let the set S consist of either an edge contraction or a vertex deletion. As all these problems are NP-complete for general graphs even if d is fixed, we restrict the input graph G to some special graph class. We continue a line of research that considers these problems for subclasses of perfect graphs, but our main results are full classifications, from a computational complexity point of view, for graph classes characterized by forbidding a single induced connected subgraph H