The Cuckoo Search algorithm (CS) still has some shortcomings, such as insufficient global search capability, challenges in exploring values beyond local optima, and underutilization of effective information within pop...
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Federated graph learning (FGL) enables clients to collaboratively train a robust graph neural network (GNN) while ensuring their private graph data never leaves the local. However, existing FGL frameworks require all ...
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Recent advancements in language models have greatly improved dialogue systems, but they still face challenges in generating personalized responses that are consistent with the user's persona and dialogue context. ...
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The increaing significance of plant life and botanical expertise extends beyond mere visual appreciation. With the growing interest in sustainable living and alternative remedies, there is a pressing demand for easily...
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Detecting sarcasm in social media presents challenges in natural language processing (NLP) due to the informal language, contextual complexities, and nuanced expression of sentiment. Integrating sentiment analysis (SA...
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The process of converting natural language requirements and visual models into executable software code remains an ongoing challenge in software engineering. We developed an intelligent system that adopts Natural Lang...
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Given a graph G=(V,E) and a set T={(si,ti):1≤i≤k}⊆V×V of k pairs, the k-Vertex-Disjoint-Paths (resp. k-Edge-Disjoint-Paths) problem asks to determine whether there exist k pairwise vertex-disjoint (resp. e...
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ISBN:
(纸本)9783031813955
Given a graph G=(V,E) and a set T={(si,ti):1≤i≤k}⊆V×V of k pairs, the k-Vertex-Disjoint-Paths (resp. k-Edge-Disjoint-Paths) problem asks to determine whether there exist k pairwise vertex-disjoint (resp. edge-disjoint) paths P1,P2,…,Pk in G such that, for each 1≤i≤k, Pi connects si to ti. Both the edge-disjoint and vertex-disjoint versions in undirected graphs are famously known to be FPT (parameterized by k) due to the Graph Minor Theory of Robertson and Seymour. Eilam-Tzoreff [DAM ‘98] introduced a variant, known as the k-Disjoint-Shortest-Paths problem, where each path is further required to be a shortest path connecting its pair. They showed that the k-Disjoint-Shortest-Paths problem is NP-complete on both directed and undirected graphs;this holds even if the graphs are planar and have unit edge lengths. We focus on four versions of the problem, corresponding to considering edge/vertex disjointness, and to considering directed/undirected graphs. Building on the reduction of Chitnis [SIDMA ’23] for k-Edge-Disjoint-Paths on planar DAGs, we obtain the following inapproximability lower bound for each of the four versions of k-Disjoint-Shortest-Paths on n-vertex graphs:Under the gap version of the Exponential Time Hypothesis (Gap-ETH), there exists a constant δ>0 such that for any constant 0δ·k time. Under the gap version of the Exponential Time Hypothesis (Gap-ETH), there exists a constant δ>0 such that for any constant 0δ·k time. We provide a single, unified framework to obtain lower bounds for each of the four versions of k-Disjoint-Shortest-Paths. We are able to further strengthen our results by restricting the structure of the input graphs in the lower bound constructions as follows:Directed: The inapproximability lower bound for edge-disjoint (resp. vertex-disjoint) paths holds even if the input graph is a planar (resp. 1-planar) DAG with max in-degree and max out-degree at most ***: The inapproximability lower bound for edge-disjoint (resp. vertex-dis
Time-Sensitive Networking (TSN) has recently become an important standard to support time-sensitive reliable low-latency data transmission in industrial and real-time applications. This work explores the use of differ...
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Underwater environments present unique challenges for image analysis due to light attenuation, scattering, and color distortion, which significantly degrade image quality. These facts make simple operations such as im...
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The current research work proposes a difficultydriven comparison of three most visited automobile websites namely the Automobile Site1, Automobile Site2, Automobile Site3 on parameters including performance, Search en...
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