Related papers: Solving Minimum k-supplier in Adleman-Lipton model
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It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
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Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…
This paper targets to a novel but practical recommendation problem named exact-K recommendation. It is different from traditional top-K recommendation, as it focuses more on (constrained) combinatorial optimization which will optimize to…
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the…
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We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a…
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In this paper, we propose to study on sufficient control of complex networks which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the…
The minimum-cost subset $k$-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph $G=(V,E)$ with costs on edges and a set of terminals…
We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…
We present randomized algorithms for some well-studied, hard combinatorial problems: the k-path problem, the p-packing of q-sets problem, and the q-dimensional p-matching problem. Our algorithms solve these problems with high probability in…
The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
We give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; (3) $k$-means in…
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