18 research outputs found
Capacitated Vehicle Routing with Non-Uniform Speeds
The capacitated vehicle routing problem (CVRP) involves distributing
(identical) items from a depot to a set of demand locations, using a single
capacitated vehicle. We study a generalization of this problem to the setting
of multiple vehicles having non-uniform speeds (that we call Heterogenous
CVRP), and present a constant-factor approximation algorithm.
The technical heart of our result lies in achieving a constant approximation
to the following TSP variant (called Heterogenous TSP). Given a metric denoting
distances between vertices, a depot r containing k vehicles with possibly
different speeds, the goal is to find a tour for each vehicle (starting and
ending at r), so that every vertex is covered in some tour and the maximum
completion time is minimized. This problem is precisely Heterogenous CVRP when
vehicles are uncapacitated.
The presence of non-uniform speeds introduces difficulties for employing
standard tour-splitting techniques. In order to get a better understanding of
this technique in our context, we appeal to ideas from the 2-approximation for
scheduling in parallel machine of Lenstra et al.. This motivates the
introduction of a new approximate MST construction called Level-Prim, which is
related to Light Approximate Shortest-path Trees. The last component of our
algorithm involves partitioning the Level-Prim tree and matching the resulting
parts to vehicles. This decomposition is more subtle than usual since now we
need to enforce correlation between the size of the parts and their distances
to the depot
Does Compressed Sensing Improve the Throughput of Wireless Sensor Networks?
Although compressed sensing (CS) has been envisioned as a useful technique to improve the performance of wireless sensor networks (WSNs), it is still not very clear how exactly it will be applied and how big the improvements will be. In this paper, we propose two different ways (plain-CS and hybrid-CS) of applying CS to WSNs at the networking layer, in the form of a particular data aggregation mechanism. We formulate three flow-based optimization problems to compute the throughput of the non-CS, plain-CS, and hybrid-CS schemes. We provide the exact solution to the first problem corresponding to the non-CS case and lower bounds for the cases with CS. Our preliminary numerical results are only for a low-power regime. They illustrate two crucial insights: first, applying CS naively may not bring any improvement, and secondly, our hybrid-CS can achieve significant improvement in throughput.Published versio
Minimum Makespan Multi-vehicle Dial-a-Ride
Dial a ride problems consist of a metric space (denoting travel time between
vertices) and a set of m objects represented as source-destination pairs, where
each object requires to be moved from its source to destination vertex. We
consider the multi-vehicle Dial a ride problem, with each vehicle having
capacity k and its own depot-vertex, where the objective is to minimize the
maximum completion time (makespan) of the vehicles. We study the "preemptive"
version of the problem, where an object may be left at intermediate vertices
and transported by more than one vehicle, while being moved from source to
destination. Our main results are an O(log^3 n)-approximation algorithm for
preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation
for its special case when there is no capacity constraint. We also show that
the approximation ratios improve by a log-factor when the underlying metric is
induced by a fixed-minor-free graph.Comment: 22 pages, 1 figure. Preliminary version appeared in ESA 200
Large-Scale Multi-Robot Coverage Path Planning via Local Search
We study graph-based Multi-Robot Coverage Path Planning (MCPP) that aims to
compute coverage paths for multiple robots to cover all vertices of a given 2D
grid terrain graph . Existing graph-based MCPP algorithms first compute a
tree cover on -- a forest of multiple trees that cover all vertices -- and
then employ the Spanning Tree Coverage (STC) paradigm to generate coverage
paths on the decomposed graph of the terrain graph by circumnavigating
the edges of the computed trees, aiming to optimize the makespan (i.e., the
maximum coverage path cost among all robots). In this paper, we take a
different approach by exploring how to systematically search for good coverage
paths directly on . We introduce a new algorithmic framework, called
LS-MCPP, which leverages a local search to operate directly on . We propose
a novel standalone paradigm, Extended-STC (ESTC), that extends STC to achieve
complete coverage for MCPP on any decomposed graphs, even those resulting from
incomplete terrain graphs. Furthermore, we demonstrate how to integrate ESTC
with three novel types of neighborhood operators into our framework to
effectively guide its search process. Our extensive experiments demonstrate the
effectiveness of LS-MCPP, consistently improving the initial solution returned
by two state-of-the-art baseline algorithms that compute suboptimal tree covers
on , with a notable reduction in makespan by up to 35.7\% and 30.3\%,
respectively. Moreover, LS-MCPP consistently matches or surpasses the results
of optimal tree cover computation, achieving these outcomes with orders of
magnitude faster runtime, thereby showcasing its significant benefits for
large-scale real-world coverage tasks.Comment: Accepted to AAAI 202