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In online interval scheduling, the input is an online sequence of intervals, and the goal is to accept a maximum number of non-overlapping intervals. In the more general disjoint path allocation problem, the input is a sequence of requests,…
Orienteering is the following optimization problem: given an edge-weighted graph (directed or undirected), two nodes s,t and a time limit T, find an s-t walk of total length at most T that maximizes the number of distinct nodes visited by…
We describe a model that enables us to analyze the running time of an algorithm in a computer with a memory hierarchy with limited associativity, in terms of various cache parameters. Our model, an extension of Aggarwal and Vitter's I/O…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
{\em Personalized PageRank (PPR)} stands as a fundamental proximity measure in graph mining. Since computing an exact SSPPR query answer is prohibitive, most existing solutions turn to approximate queries with guarantees. The…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
PageRank is a widely used centrality measure that assesses the significance of vertices in a graph by considering their connections and the importance of those connections. Efficiently updating PageRank on dynamic graphs is essential for…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
Range-filtering approximate nearest neighbor (RFANN) search is attracting increasing attention in academia and industry. Given a set of data objects, each being a pair of a high-dimensional vector and a numeric value, an RFANN query with a…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them…
Direct Preference Optimization (DPO) aligns language models using pairwise preference comparisons, offering a simple and effective alternative to Reinforcement Learning (RL) from human feedback. However, in many practical settings, training…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems. There have been recent efforts to generalize SRG analysis to Multiple-Input Multiple-Output (MIMO) systems. However,…
WiFi received signal strength (RSS) environment evolves over time due to movement of access points (APs), AP power adjustment, installation and removal of APs, etc. We study how to effectively update an existing database of fingerprints,…
In this paper, we address the problem of scheduling a set of robots to complete tasks in a laboratory environment, modelled as a graph, while avoiding collisions. We analyze the dynamic programming algorithm (PA) introduced in…
In large-scale traffic optimization, models based on Macroscopic Fundamental Diagram (MFD) are recognized for their efficiency in broad network analyses. However, they fail to reflect variations in the individual traffic status of each road…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the…
A temporal graph is a graph in which the edge set can change from one time step to the next. The temporal graph exploration problem TEXP is the problem of computing a foremost exploration schedule for a temporal graph, i.e., a temporal walk…
Given a large graph, how can we determine similarity between nodes in a fast and accurate way? Random walk with restart (RWR) is a popular measure for this purpose and has been exploited in numerous data mining applications including…
Recurrent neural networks have shown remarkable success in modeling sequences. However low resource situations still adversely affect the generalizability of these models. We introduce a new family of models, called Lattice Recurrent Units…