This talk describes a new graph-pattern engine called Jedi. Using a recent simplification of worst-case optimal join algorithms due to Ngo et al., Jedi translates join queries into a series of set intersection and union operations. Such set operations are ideally suited to modern CPUs that provides single-instruction, multiple data (SIMD) instructions. Using these ideas, we demonstrate that Jed...

let g be a simple connected graph. the first and second zagreb indices have been introducedas  vv(g)(v)2 m1(g) degg and m2(g)  uve(g)degg(u)degg(v) , respectively,where degg v(degg u) is the degree of vertex v (u) . in this paper, we define a newdistance-based named hyperzagreb as e uv e(g) .(v))2 hm(g)     (degg(u)  degg inthis paper, the hyperzagreb index of the cartesian product...

Let G be a simple connected graph. The first and second Zagreb indices have been introduced as  vV(G) (v)2 M1(G) degG and M2(G)  uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G)     (degG(u)  degG In this paper, the HyperZagreb index of the Cartesian p...

Let G = (V, E) be a graph and a weight function w : E -+ Z+. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. A T-join is a minimal subset of edges that meets every T-cut (a generalization of solutionS to the Chinese postman problem). The main theorem of this paper gives a tight upper bound on the difference between the ...

Probability is a useful tool for reasoning when faced with uncertainty. Bayesian networks offer a compact representation of a probabilistic problem, exploiting independence amongst variables that allows a factorization of the joint probability into much smaller local probability distributions. The standard approach to probabilistic inference in Bayesian networks is to compile the graph into a j...

It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition multiplication, respectively. This led to new characterization of Shannon capacity $\Theta$ via Strassen's Positivstellensatz: $\Theta(\bar{G}) = \inf_f f(G)$, where $f : \mathsf{Graph} \to \mathbb{R}_+$ r...

Let G be a connected graph whose least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We show first that either G is complete or λ(G) is a simple eigenvalue. In the latter case, the sign pattern of a corresponding eigenvector determines a partition of the vertex set, and we study the structure of G in terms of this partition. We find that G is either biparti...

The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to deduce further properties of q(G). It is shown that there is a great number of graphs G for which q(G) = 2. For some families of graphs, such as the join of a graph with itself,...

This paper introduces the Tuple Graph (TuG) synopses, a new class of data summaries that enable accurate selectivity estimates for complex relational queries. The proposed summarization framework adopts a “semi-structured” view of the relational database, modeling a relational data set as a graph of tuples and join queries as graph traversals respectively. The key idea is to approximate the str...

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...