We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an α-approximation for the minimum directed kspanner problem for k ≥ 5 requires Ω(n/ √ α log n) rounds using deterministic algorithms or Ω( √ n/ √ α log n) rounds us...

Many optimization problems including the network design problem of finding the bounded diameter minimum spanning tree are computationally intractable. Therefore, a practical approach for solving such problems is to employ heuristic algorithms that can find solution close to the optimal one within a reasonable amount of time. Neighborhood search algorithms are a wide class of algorithms where at...

A key challenge in developing efficient local search solvers is to effectively minimise search stagnation (i.e. avoiding traps or local minima). A majority of the state-of-the-art local search solvers perform random and/or Novelty-based walks to overcome search stagnation. Although such strategies are effective in diversifying a search from its current local minimum, they do not actively preven...

this paper presents a rational haar wavelet operational method for solving the inverse laplace transform problemand improves inherent errors from irrational haar wavelet. the approach is thus straightforward, rather simple andsuitable for computer programming. we define that $p$ is the operational matrix for integration of the orthogonalhaar wavelet. simultaneously, simplify the formulaes of li...

a computational study of the electronic structure and stability of complexes formed between zeolite y and boric acid was carried out at the hf and b3lyp levels using 6-31g* basis set. five structures located as local minimum in pes of complex (structures d, e, f, g, and h). the most stable structure is formed due to hydrogen bonding between two hydroxyl of boric acid and both oxygen of ...

We present a simple 3-approximation algorithm for minimum-weight dominating set and minimum-weight vertex cover in unit-disk graphs and quasi unit-disk graphs in which each node knows its coordinates. The algorithm is local: the output of a node depends solely on the input within its constantradius neighbourhood. The local horizon of the algorithm is small, both in the worst case and on average.

We show that very simple algorithms based on local search are polynomial-time approximation schemes for Maximum Independent Set, Minimum Vertex Cover and Minimum Dominating Set, when the input graphs have a fixed forbidden minor.

In this paper, we consider an optimization problem arising in multidimensional scaling with city-block distances. The objective function of this problem has many local minimum points and may be even non-differentiable at a minimum point. We reformulate the problem into a problem with convex quadratic objective function, linear and complementarity constraints. In addition, we propose an algorith...

Local algorithms for obtaining pivot orderings for sparse symmetric coefficient matrices are reviewed together with their mathematical background, appropriate data structures and details of efficient implementation. Heuristics that go beyond the classical Minimum Degree and Minimum Local Fill scoring functions are discussed, illustrated, improved and extensively tested on a test suite of matric...

The vertex-connectivity and edge-connectivity of the zero-divisor graph associated to a finite commutative ring are studied. It is shown that the edgeconnectivity of ΓR always coincides with the minimum degree. When R is not local, it is shown that the vertex-connectivity also equals the minimum degree, and when R is local, various upper and lower bounds are given for the vertex-connectivity.