Pedestrian trajectory prediction is important in the research of mobile robot navigation in environments with pedestrians. Most pedestrian trajectory prediction algorithms require the input historical trajectories to ...
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Random generation of shortest paths in graphs is utilized across various domains, including traffic-flow simulation and network topology exploration. In this paper, we address the challenge of uniform shortest path sa...
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A triangle-free (simple) 2-matching is an edge set that has at most 2 edges incident to each vertex and contains no cycle of length 3. For the problem of finding a maximum cardinality triangle-free 2-matching in a giv...
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Multi-armed bandits (MABs) are frequently used for online sequential decision-making in applications ranging from recommending personalized content to assigning treatments to patients. A recurring challenge in the app...
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Distributed optimization aims to leverage the local computation and communication capabilities of each agent to achieve a desired global objective. This paper addresses the distributed pose graph optimization (PGO) pr...
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In node classification tasks, traditional methods like LPA-GCN struggle with scalability and sensitivity to label noise. We propose LPA-graphSAGE, combining the Label Propagation Algorithm with graphSAGE’s ...
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We consider the problem of vertex recoloring: we are given n vertices with their initial coloring, and edges arrive in an online fashion. The algorithm is required to maintain a valid coloring by means of vertex recol...
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ISBN:
(纸本)9783959773652
We consider the problem of vertex recoloring: we are given n vertices with their initial coloring, and edges arrive in an online fashion. The algorithm is required to maintain a valid coloring by means of vertex recoloring, where recoloring a vertex incurs a cost. The problem abstracts a scenario of job placement in machines (possibly in the cloud), where vertices represent jobs, colors represent machines, and edges represent "anti affinity" (disengagement) constraints. Online coloring in this setting is a hard problem, and only a few cases were analyzed. One family of instances which is fairly well-understood is bipartite graphs, i.e., instances in which two colors are sufficient to satisfy all constraints. In this case it is known that the competitive ratio of vertex recoloring is Θ(log n). In this paper we propose a generalization of the problem, which allows using additional colors (possibly at a higher cost), to improve overall performance. Concretely, we analyze the simple case of bipartite graphs of bounded largest bond (a bond of a connected graph is an edge-cut that partitions the graph into two connected components). From the upper bound perspective, we propose two algorithms. One algorithm exhibits a trade-off for the uniform-cost case: given Ω(log β) ≤ c ≤ O(log n) colors, the algorithm guarantees that its cost is at most O(logcn ) times the optimal offline cost for two colors, where n is the number of vertices and β is the size of the largest bond of the graph. The other algorithm is designed for the case where the additional colors come at a higher cost, D > 1: given ∆ additional colors, where ∆ is the maximum degree in the graph, the algorithm guarantees a competitive ratio of O(log D). From the lower bounds viewpoint, we show that if the cost of the extra colors is D > 1, no algorithm (even randomized) can achieve a competitive ratio of o(log D). We also show that in the case of general bipartite graphs (i.e., of unbounded bond size), any determinist
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a mor...
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We consider an unsplittable version of the minimum max-load multicommodity flow problem, where each demand must be routed along a single path. The objective is to minimize the maximum load on any edge in the network. ...
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A set S⊆V(G) is said to be a hop dominating set if every vertex u∈V(G)\S, there exists a vertex v∈S such that d(u,v)=2 where d(u, v) represents the distance between u and v in G. The minimum k for which there e...
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