We consider the problem of pattern matching with k mismatches, where there can be don't care or wild card characters in the pattern. Specifically, given a pattern P of length m and a text T of length n, we want to find all occurrences of P in T that have no more than k mismatches. The pattern can have don't care characters, which match any character. Without don't cares, the best known algorith...

Let $G=(V_G, E_G)$ be a simple and connected graph. A set $M\subseteq E_G$ is called matching of $G$ if no two edges $M$ are adjacent. The number in its size. maximal it cannot extended to larger $G$. smallest size the saturation In this paper we concerned with numbers lexicographic product graphs. We also address solve an open problem about maximum matchings graphs given degree $\Delta$.

Let D=(V,A) be a digraphs without isolated vertices. The first Zagreb index of digraph D is defined as summation over all arcs, M1(D)=12∑uv∈A(du++dv−), where du+(resp. du−) denotes the out-degree (resp. in-degree) vertex u. In this paper, we give maximal values and set orientations unicyclic graphs with n vertices matching number m (2≤m≤⌊n2⌋).

We present O(log logn)-round algorithms in the Massively Parallel Computation (MPC) model, with Õ(n) memory per machine, that compute a maximal independent set, a 1 + ε approximation of maximum matching, and a 2+ ε approximation of minimum vertex cover, for any n-vertex graph and any constant ε > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log∆)...

A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups. 1. Background and results Let P be a partially order...

We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A,B,C ⊆ X with A∪B∪C = X and |A|, |B|, |C| ≤ k such that any subset of X that is a minimal separator of H is a subset of either A,B or C. Treewidth and branchwidth have alternative definitions through inte...

Abstract Finite State Machines with Input Multiplexing (FSMIMs) were proposed in previous work as a technique for efficient mapping (FSMs) into ROM memory. In this paper, we present new contributions to the optimization process involved implementation of FSMIMs Field Programmable Gate Array (FPGA) devices. This consists two stages: (1) simplification bank input selectors FSMIM, and (2) reductio...

We characterize the set of stable matchings when individuals are farsighted and they choose their objections optimally along a objection path. use solution concept called maximal (MFS), which is an adaptation concepts developed in Dutta Vohra (2017) Vartiainen (2020) to one-to-one matching problems. MFS always exists, but it need not be unique. There unique largest that contains all other, equa...