4 research outputs found
Collaborative Delivery with Energy-Constrained Mobile Robots
We consider the problem of collectively delivering some message from a
specified source to a designated target location in a graph, using multiple
mobile agents. Each agent has a limited energy which constrains the distance it
can move. Hence multiple agents need to collaborate to move the message, each
agent handing over the message to the next agent to carry it forward. Given the
positions of the agents in the graph and their respective budgets, the problem
of finding a feasible movement schedule for the agents can be challenging. We
consider two variants of the problem: in non-returning delivery, the agents can
stop anywhere; whereas in returning delivery, each agent needs to return to its
starting location, a variant which has not been studied before.
We first provide a polynomial-time algorithm for returning delivery on trees,
which is in contrast to the known (weak) NP-hardness of the non-returning
version. In addition, we give resource-augmented algorithms for returning
delivery in general graphs. Finally, we give tight lower bounds on the required
resource augmentation for both variants of the problem. In this sense, our
results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the
23rd International Colloquium on Structural Information and Communication
Complexity 2016, SIROCCO'1
Collective fast delivery by energy-efficient agents
We consider k mobile agents initially located at distinct nodes of an
undirected graph (on n nodes, with edge lengths) that have to deliver a single
item from a given source node s to a given target node t. The agents can move
along the edges of the graph, starting at time 0 with respect to the following:
Each agent i has a weight w_i that defines the rate of energy consumption while
travelling a distance in the graph, and a velocity v_i with which it can move.
We are interested in schedules (operating the k agents) that result in a
small delivery time T (time when the package arrives at t), and small total
energy consumption E. Concretely, we ask for a schedule that: either (i)
Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast
delivery), or (iii) Minimizes epsilon*T + (1-epsilon)*E, for a given epsilon,
0<epsilon<1.
We show that (i) is solvable in polynomial time, and show that (ii) is
polynomial-time solvable for uniform velocities and solvable in time O(n + k
log k) for arbitrary velocities on paths, but in general is NP-hard even on
planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We
show that there is a 3-approximation algorithm for (iii) using a single agent.Comment: In an extended abstract of this paper [MFCS 2018], we erroneously
claimed the single agent approach for variant (iii) to have approximation
ratio