A note on approximating the min–max vertex disjoint paths on directed acyclic graphs

AbstractThis paper shows that the FPTAS for the min–max disjoint paths problem on directed acyclic graphs by Yu et al. (2010) [7] can be improved by a rounding and searching technique

Approximation algorithms for the shortest total path length spanning tree problem

AbstractGiven an undirected graph with a nonnegative weight on each edge, the shortest total path length spanning tree problem is to find a spanning tree of the graph such that the total path length summed over all pairs of the vertices is minimized. In this paper, we present several approximation algorithms for this problem. Our algorithms achieve approximation ratios of 2, 15/8, and 3/2 in time O(n2+f(G)),O(n3), and O(n4) respectively, in which f(G) is the time complexity for computing all-pairs shortest paths of the input graph G and n is the number of vertices of G. Furthermore, we show that the approximation ratio of (4/3+ε) can be achieved in polynomial time for any constant ε>0

The maximum disjoint paths problem on multi-relations social networks

Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint uni-color paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both approximation and exact algorithms are proposed. Since short paths are much more significant in SNA, we also study the length-bounded version of the problem, in which the lengths of paths are required to be upper bounded by a fixed integer $l$. It is shown that the problem can be solved in polynomial time for $l=3$ and is NP-hard for $l\geq 4$. We also show that the problem can be approximated with ratio $(l-1)/2+\epsilon$ in polynomial time for any $\epsilon >0$. Particularly, for $l=4$, we develop an efficient 2-approximation algorithm

Improving Medical Report Generation with Adapter Tuning and Knowledge Enhancement in Vision-Language Foundation Models

Medical report generation demands automatic creation of coherent and precise descriptions for medical images. However, the scarcity of labelled medical image-report pairs poses formidable challenges in developing large-scale neural networks capable of harnessing the potential of artificial intelligence, exemplified by large language models. This study builds upon the state-of-the-art vision-language pre-training and fine-tuning approach, BLIP-2, to customize general large-scale foundation models. Integrating adapter tuning and a medical knowledge enhancement loss, our model significantly improves accuracy and coherence. Validation on the dataset of ImageCLEFmedical 2023 demonstrates our model's prowess, achieving the best-averaged results against several state-of-the-art methods. Significant improvements in ROUGE and CIDEr underscore our method's efficacy, highlighting promising outcomes for the rapid medical-domain adaptation of the vision-language foundation models in addressing challenges posed by data scarcity