Related papers: Finding Optimal Longest Paths by Dynamic Programmi…
Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation in processing graphs. Recently, size, variety, and structural complexity of these networks has grown dramatically.…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can…
Planning long-horizon robot manipulation requires making discrete decisions about which objects to interact with and continuous decisions about how to interact with them. A robot planner must select grasps, placements, and motions that are…
All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
This paper proposes a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments. A novel concept of Time-Warped Grid is introduced to predict the pose of obstacles in the environment and avoid…
The dual of a planar graph $G$ is a planar graph $G^*$ that has a vertex for each face of $G$ and an edge for each pair of adjacent faces of $G$. The profound relationship between a planar graph and its dual has been the algorithmic basis…
The constrained path optimization (CPO) problem takes the following input: (a) a road network represented as a directed graph, where each edge is associated with a "cost" and a "score" value; (b) a source-destination pair and; (c) a budget…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
The problem of identifying the k-shortest paths KSPs for short in a dynamic road network is essential to many location-based services. Road networks are dynamic in the sense that the weights of the edges in the corresponding graph…
Modern graphs are both large and dynamic, presenting significant challenges for fundamental queries, such as the Single-Source Shortest Path (SSSP) problem. Naively recomputing the SSSP tree after each topology change is prohibitively…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…