
Graph Exploration by EnergySharing Mobile Agents
We consider the problem of collective exploration of a known nnode edge...
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Evacuation of equilateral triangles by mobile agents of limited communication range
We consider the problem of evacuating k ≥ 2 mobile agents from a unitsi...
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Gathering in 1Interval Connected Graphs
We examine the problem of gathering k ≥ 2 agents (or multiagent rendezv...
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ConsenusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
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ConsensusHalving: Does it Ever Get Easier?
In the εConsensusHalving problem, a fundamental problem in fair divisi...
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Reallocating Multiple Facilities on the Line
We study the multistage Kfacility reallocation problem on the real line...
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Efficient Splitting of Measures and Necklaces
We provide approximation algorithms for two problems, known as NECKLACE ...
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The Bike Sharing Problem
Assume that m ≥ 1 autonomous mobile agents and 0 ≤ b ≤ m singleagent transportation devices (called bikes) are initially placed at the left endpoint 0 of the unit interval [0,1]. The agents are identical in capability and can move at speed one. The bikes cannot move on their own, but any agent riding bike i can move at speed v_i > 1. An agent may ride at most one bike at a time. The agents can cooperate by sharing the bikes; an agent can ride a bike for a time, then drop it to be used by another agent, and possibly switch to a different bike. We study two problems. In the problem, we require all agents and bikes starting at the left endpoint of the interval to reach the end of the interval as soon as possible. In the problem, we aim to minimize the arrival time of the agents; the bikes can be used to increase the average speed of the agents, but are not required to reach the end of the interval. Our main result is the construction of a polynomial time algorithm for the problem that creates an arrivaltime optimal schedule for travellers and bikes to travel across the interval. For the problem, we give an algorithm that gives an optimal solution for the case when at most one of the bikes can be abandoned.
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