相关论文: Geometric Localization of Homology Cycles
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Given a graph, the general problem to cover the maximum number of vertices by a collection of vertex-disjoint long paths seemingly escapes from the literature. A path containing at least $k$ vertices is considered long. When $k \le 3$, the…
We consider a single allocation hub-and-spoke network design problem which allocates each non-hub node to exactly one of given hub nodes so as to minimize the total transportation cost. This paper deals with a case in which the hubs are…
We study the following generalization of the Hamiltonian cycle problem: Given integers $a,b$ and graph $G$, does there exist a closed walk in $G$ that visits every vertex at least $a$ times and at most $b$ times? Equivalently, does there…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
In multistage perfect matching problems we are given a sequence of graphs on the same vertex set and asked to find a sequence of perfect matchings, corresponding to the sequence of graphs, such that consecutive matchings are as similar as…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given graph, and of the existence of a truth assignment satisfying a given Boolean formula $C$, are well-known {\it NP}-complete problems. Here we…
We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specified graphs, many of which are PSPACE-complete. Assuming P != PSPACE, the existence or nonexistence of such efficient…
Computational topology provides a tool, persistent homology, to extract quantitative descriptors from structured objects (images, graphs, point clouds, etc). These descriptors can then be involved in optimization problems, typically as a…
A graph G is locally isometric if the subgraph induced by the neighbourhood of every vertex is an isometric subgraph of G. It is shown that the hamilton cycle problem for locally isometric graphs with maximum degree at most 8 is…
Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given…
Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…