A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708–717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio 2, by a primal-d...
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ISBN:
(纸本)9783031813955
A classic result of Williamson, Goemans, Mihail, and Vazirani [STOC 1993: 708–717] states that the problem of covering an uncrossable set family by a min-cost edge set admits approximation ratio 2, by a primal-dual algorithm with a reverse delete phase. Recently, Bansal, Cheriyan, Grout, and Ibrahimpur [ICALP 2023: 15:1-15:19] showed that this algorithm achieves approximation ratio 16 for a larger class of so called γ-pliable set families, that have much weaker uncrossing properties. In this paper we will improve the approximation ratio to 10. Using this result and other techniques, we also improve approximation ratios for the following two problems related to the Capacitatedk-Edge Connected Spanning Subgraph (Cap-k-ECSS) problem. Near Min-Cuts Cover: Given a graph G0=(V,E0) and an edge set E on V with costs, find a min-cost edge set J⊆E that covers all cuts with at most k-1 edges of the graph G0. We improve the approximation ratio from 16 to 10. We also obtain approximation ratio k-λ0+1+ϵ, where λ0 is the edge connectivity of G0, which is better than ratio 10 when k-λ0≤8.(k, q)-Flexible Graph Connectivity ((k, q)-FGC): Given a graph G=(V,E) with edge costs, a set U⊆E of "unsafe" edges, and integers k, q, find a min-cost subgraph H of G such that every cut of H has at least k safe edges or at least k+q edges. We will show that (k, 1)-FGC admits approximation ratio 3.5+ϵ if k is odd (improving previous ratio 4), that (k, 2)-FGC admits approximation ratio 7+ϵ (improving previous ratio 20), and that (k, 3)-FGC admits approximation ratio 16 for k even (improving previous ratio 22). We also show that for unit costs, (k, q)-FGC admits approximation ratio α+2qk, where α≈1+O(1/k) is an approximation ratio for the Min-Sizek-Edge-Connected Spanning Subgraph problem. Near Min-Cuts Cover: Given a graph G0=(V,E0) and an edge set E on V with costs, find a min-cost edge set J⊆E that covers all cuts with at most k-1 edges of the graph G0. We improve the approximation ratio from 16
The Knapsack Median problem was known to be W[2]-hard if parameterized by the maximal number of opened facilities in feasible solutions (denoted by k), implying that exactly solving this problem in FPT(k) time is unli...
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Given an undirected graph G=(V,E) with weighted vertices and edges, a set J of n=|V| independent jobs and m unrelated machines, each vertex v∈V corresponds to a job Jj∈J. The combination of prize-collecting vertex c...
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Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. Starting from a fixed root node, an expanding search visits the vertices sequentially until it...
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Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. Starting from a fixed root node, an expanding search visits the vertices sequentially until it finds the target, where the next vertex can be reached from any of the previously visited vertices. That is, the time to reach the next vertex equals the shortest-path distance from the set of all previously visited vertices. The expanding search problem then asks for a sequence of the nodes, so as to minimize the expected time to finding the target. This problem has numerous applications, such as searching for hidden explosives, mining coal, and disaster relief. In this paper, we develop exact algorithms and heuristics, including a branch-and-cut procedure, a greedy algorithm with a constant-factor approximation guarantee, and a local search procedure based on a spanning-tree neighborhood. Computational experiments show that our branch-and-cut procedure outperforms existing methods for instances with nonuniform probability distributions and that both our heuristics compute near-optimal solutions with little computational effort. Summary of Contribution: This paper studies new algorithms for the expanding search problem, which asks to search a graph for a target hidden in one of the nodes according to a known probability distribution. This problem has applications such as searching for hidden explosives, mining coal, and disaster relief. We propose several new algorithms, including a branch-and-cut procedure, a greedy algorithm, and a local search procedure;and we analyze their performance both experimentally and theoretically. Our analysis shows that the algorithms improve on the performance of existing methods and establishes the first constant-factor approximation guarantee for this problem.
In this paper we obtain improved approximation algorithms for the Capacitated Min-Max Graph Cover Problems and the first constant-factor approximation algorithms for the Capacitated Minimum Graph Cover Problems. These...
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Convolutional neural networks (CNNs) have achieved immense success in computer vision and other field of science. Despite the achievements, state-of-the-art CNN models have grown to gigantic sizes that demand a lot of...
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ISBN:
(数字)9798331509712
ISBN:
(纸本)9798331509729
Convolutional neural networks (CNNs) have achieved immense success in computer vision and other field of science. Despite the achievements, state-of-the-art CNN models have grown to gigantic sizes that demand a lot of computing power and memory resources. As a model compression technique, parameter pruning can lower the computation and memory a CNN model needs. Previous work has proposed a parameter pruning method, which compresses the neural networks by eliminating the rows and columns of the weight matrices. Removing rows and columns preserves the dense structure of the weight matrix, rather than the sparse structure produced by unstructured pruning. Although row-and-column pruning effectively reduces the model size, making the model as compact as possible without sacrificing accuracy remains a challenge. We prove that the row-and-column pruning problem is an NP-complete problem, and we propose two approximation algorithms that provide solutions within twice the cost of the optimal solution. We also show that the approximation ratio cannot be improved for these two algorithms. Finally, we propose two schemes based on simulated annealing to solve the row-and-column pruning problem. The two proposed schemes improve accuracy by 2.7% and 1.6%, respectively, on the ResNet-18 model with 93% sparsity using the Food-101 dataset.
The freeze tag problem (FTP) aims to awaken a swarm of robots with one or more initial awake robots as soon as possible. Each awake robot must touch a sleeping robot to wake it up. Once a robot is awakened, it can ass...
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The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-known variant of the classic Capacitated Vehicle Routing Problem (CVRP), where we need to route capacitated vehicles located in multiple depots to s...
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We address the problem on uniform parallel batch machines to minimize makespan where each job is restricted to a specific subset of machines, known as its processing set. Batch machines have diverse speeds and capacit...
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We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it Bounded Acceleration SPP (BASP). This variant is inspired by an indus...
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We introduce a variant of the Shortest Path Problem (SPP), in which we impose additional constraints on the acceleration over the arcs, and call it Bounded Acceleration SPP (BASP). This variant is inspired by an industrial application: a vehicle needs to travel from its current position to a target one in minimum-time, following pre-defined geometric paths connecting positions within a facility, while satisfying some speed and acceleration constraints depending on the vehicle position along the currently traveled path. We characterize the complexity of BASP, proving its NP-hardness. We also show that, under additional hypotheses on problem data, the problem admits a pseudo-polynomial time-complexity algorithm. Moreover, we present an approximation algorithm with polynomial time-complexity with respect to the data of the original problem and the inverse of the approximation factor e. Finally, we present some computational experiments to evaluate the performance of the proposed approximation algorithm.
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