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

The Max-Distance Network Creation Game on General Host Graphs

In this paper we study a generalization of the classic \emph{network creation game} to the scenario in which the $n$ players sit on a given arbitrary \emph{host graph}, which constraints the set of edges a player can activate at a cost of $\alpha \geq 0$ each. This finds its motivations in the physical limitations one can have in constructing links in the practice, and it has been studied in the past only when the routing cost component of a player is given by the sum of distances to all the other nodes. Here, we focus on another popular routing cost, namely that which takes into account for each player its \emph{maximum} distance to any other player. For this version of the game, we first analyze some of its computational and dynamic aspects, and then we address the problem of understanding the structure of associated pure Nash equilibria. To this respect, we show that the corresponding price of anarchy (PoA) is fairly bad, even for several basic classes of host graphs. More precisely, we first exhibit a lower bound of $\Omega \big(\sqrt{\frac{n}{1+\alpha}}\big)$ for any $\alpha = o(n)$. Notice that this implies a counter-intuitive lower bound of $\Omega(\sqrt{n})$ for the case $\alpha=0$ (i.e., edges can be activated for free). Then, we show that when the host graph is restricted to be either $k$-regular (for any constant $k \geq 3$), or a 2-dimensional grid, the PoA is still $\Omega(1+\min\{\alpha, \frac{n}{\alpha}\})$, which is proven to be tight for $\alpha=\Omega(\sqrt{n})$. On the positive side, if $\alpha \geq n$, we show the PoA is $O(1)$. Finally, in the meaningful practical case in which the host graph is very sparse (i.e., $|E(H)|=n-1+k$, with $k=O(1)$), we prove that the PoA is $O(1)$, for any $\alpha$

Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game

The Stackelberg Minimum Spanning Tree (StackMST) game is a network pricing (bilevel) optimization problem. The game is played by two players on a graph G = (V,E), whose edges are partitioned into two sets: a set R of red edges (inducing a spanning tree of G) with a fixed non-negative real cost, and a set B of blue edges which are instead priced by a leader. This is done with the final intent of maximizing a revenue that will be returned for their purchase by a follower, whose goal in turn is to select a minimum spanning tree of G. StackMST is known to be APX-hard already when the number of distinct red costs is 2, as well as min {k, 1 + ln β, 1 + ln ρ}-approximable, where k is the number of distinct red costs, β is the number of blue edges selected by the follower in an optimal pricing, and ρ is the maximum ratio between red costs. In this paper we analyze some meaningful specializations and generalizations of StackMST, which shed some more light on the computational complexity of the game. More precisely, we first show that if G is complete, then the following holds: (i) if there are only 2 distinct red costs, then the problem can be solved optimally (this contrasts with the corresponding APX-hardness of the general problem); (ii) otherwise, the problem can be approximated within 7/4 + ε, for any ε> 0. Afterwards, we define a natural extension of StackMST, namely that in which blue edges have a non-negative activation cost associated, and the leader has a global activation budget that must not be exceeded, and, after showing that the very same approximation ratio as that of the original game can be achieved, we prove that if the spanning tree induced by the red edges has radius h (in terms of number of edges), then the problem admits a (2h + ε)-approximation algorithm

Dynamic Mechanism Design

In this paper we address the question of designing truthful mechanisms for solving optimization problems on dynamic graphs. More precisely, we are given a graph G of n nodes, and we assume that each edge of G is owned by a selfish agent. The strategy of an agent consists in revealing to the system the cost for using its edge, but this cost is not constant and can change over time. Additionally, edges can enter into and exit from G. Among the various possible assumptions which can be made to model how these edge-cost modifications take place, we focus on two settings: (i) the dynamic, in which modifications are unpredictable and time-independent, and for a given optimization problem on G, the mechanism has to maintain efficiently the output specification and the payment scheme for the agents; (ii) the time-sequenced, in which modifications happens at fixed time steps, and the mechanism has to minimize an objective function which takes into consideration both the quality and the set-up cost of a new solution. In both settings, we investigate the existence of exact and approximate truthful mechanisms. In particular, for the dynamic setting, we analyze the minimum spanning tree problem, and we show that if edge costs can only decrease, then there exists an efficient dynamic truthful mechanism for handling a sequence of k edge-cost reductions having runtime, where h is the overall number of payment changes

What feeds shelf-edge clinoforms over margins deprived of adjacent land sources? An example from southeastern Brazil

In southeastern Brazil, the Serra do Mar coastal mountain range blocks the sediment influx from arriving at a ca. 1,500 km long continental margin comprising Santos and Pelotas basins. Despite this deprivation, the margin accumulated a ca. 1 km thick sedimentary succession since the Mid-Miocene. Examination of seismic reflection and oceanographic data indicates that shelf-margin clinoform formation exhibits a regional variability, with major sigmoidal clinoforms developed in the transitional area between both basins. Laterally, poorly developed oblique clinoforms constitute isolated depocenters along the shelf margin. The continuous clinoform development in the transitional area is attributed to the major influence on sediment transport patterns of several ocean bottom currents flowing along the margin, such as the Brazil Coastal Current, the Brazil Current and the Intermediate Water Brazil Current. These currents erode, transport and distribute sediments across the shelf break and upper slope from distant sediment sources located either north or south of the study area. The progressive southward strengthening of the Brazil Current could be responsible for a major southward sediment redistribution from the northern Campos Basin, and/or for sediment entrainment from northward-induced transport by the Brazil Coastal Current, originally derived from the De la Plata Estuary. In the transition between Santos and Pelotas basins, the Intermediate Water Brazil Current splits forming the Santos Bifurcation, allowing for a continuous depositional process and clinoform generation. We suggest that ocean bottom currents may shape other shelf-edge ‘contouritic clinoforms’ in continental margins mainly constructed by along-strike sediment transport largely driven by long-term geostrophic currents.Fundação de Amparo à Pesquisa do Estado de São Paulo. Grant Numbers: 2014/08266‐2, 2015/17763‐2, 2016/22194‐0 . CNPq. Grant Numbers: 401041, 2014‐0. Universidade de São Paul

Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots

International audienc

Project Games

Lecture Notes in Computer Science book series (LNCS, volume 11485)We consider a strategic game called project game where each agent has to choose a project among his own list of available projects. The model includes positive weights expressing the capacity of a given agent to contribute to a given project. The realization of a project produces some reward that has to be allocated to the agents. The reward of a realized project is fully allocated to its contributors, according to a simple proportional rule. Existence and computational complexity of pure Nash equilibria is addressed and their efficiency is investigated according to both the utilitarian and the egalitarian social function