Related papers: On Embeddability of Buses in Point Sets
Given a set of points in the plane, the \textsc{General Position Subset Selection} problem is that of finding a maximum-size subset of points in general position, i.e., with no three points collinear. The problem is known to be ${\rm…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ``planted'' solution; thus, we obtain the first rigorous…
The phasor measurement unit (PMU) placement problem is revisited by taking into account a stronger characterization of the electrical connectedness between various buses in the grid. To facilitate this study, the placement problem is…
The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimization problem with the goal to design shifts to cover prearranged bus tours. The objective takes into account the operational cost as well as the satisfaction of drivers.…
In this paper, we propose an Empirically-based Monte Carlo Bus-network (EMB) model as a test bed to simulate intervention strategies to overcome the inefficiencies of bus bunching. The EMB model is an agent-based model which utilizes the…
The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and…
We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…
We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by half-planes of both colors. This settles a problem of Keszegh.
Safely serving the school transportation demand with the minimum number of buses is one of the highest financial goals of school transportation directors. To achieve that objective, a good and efficient way to solve the routing and…
This study addresses the rebalancing of empty modular transit pods between scheduled service trips in fixed-route bus systems. A two-stage hierarchical optimization framework is proposed. The first stage determines the minimum fleet size…
In rank aggregation problems (RAP), the solution is usually a consensus ranking that generalizes a set of input orderings. There are different variants that differ not only in terms of the type of rankings that are used as input and output,…
The multi Vehicle Routing Problem with Pickup and Delivery with Time Windows is a challenging version of the Vehicle Routing Problem. In this paper, by embedding many complex assignment routing constraints through constructing a multi…
A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs…
This paper addresses the on-demand meeting-point-based feeder electric bus routing and charging scheduling problem under charging synchronization constraints. The problem considered exhibits the structure of the location routing problem,…
We study the Balanced Connected Subgraph(shortly, BCS) problem on geometric intersection graphs such as interval, circular-arc, permutation, unit-disk, outer-string graphs, etc. Given a vertex-colored graph $G=(V,E)$, where each vertex in…
This paper proposes a local path planning method with a reachable set for Automated vertical Parking Systems (APS). First, given a parking lot layout with a goal position, we define an intermediate pose for the APS to accomplish reverse…
We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks)…
Given a simple undirected graph $G=(V,E)$ and a partition of the vertex set $V$ into $p$ parts, the \textsc{Partition Coloring Problem} asks if we can select one vertex from each part of the partition such that the chromatic number of the…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…