Spectral algorithms based on matrix representations of networks are often used to detect communities, but classic spectral methods based on the adjacency matrix and its variants fail in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking ...

We present a new method to represent variable bindings in the Warren Abstract Machine (WAM), so that ages of variable bindings can be easily found using this new representation in our intelligent backtracking schema. The age of a variable bound to a non-variable term will be the youngest choice point such that backtracking to that choice point can make that variable an unbound variable again. I...

An efficient backtracking method for LISP, used in the MLISP2 language, is described. The method is optimal in the following senses: <1) Only necessary state information is saved. The backtracking system routines are sufficiently efficient to require less than ten percent of the execution time of typical jobs. (2) Most common operations — fetching/storing the value of a variable or the property...

We consider the problem of eeciently supporting backtracking in independent and-parallel non-deterministic systems. We consider this problem in the context of logic programming, although the solution proposed is suuciently general to be applicable to any non-deterministic language or system. EEcient implementation of backtracking is a diicult task, the primary reason being that backtracking is ...

Here we show how the idea of dynamic backtracking can be applied to branch and bound optimization. This is done by exploiting the concept of valued nogood introduced in [6, 16, 17]. However, simple replacement of nogoods with valued nogoods does not lead to a correct algorithm. We show that a way to achieve correctness is to use at each variable a separate nogood storage for each position that ...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...