A comparison of optimal tax policies when compensation or responsibility matter

This paper examines optimal redistribution in a model with high and low-skilled individuals with heterogeneous tastes for labor, that either work or not. With such double heterogeneity, traditional Welfarist criteria including Utilitarianism fail to take the compensation-responsibility trade-off into account. As a response, several other criteria have been proposed in the literature. This paper is the first to compare the extent to which optimal policies based on different normative criteria obey the principles of compensation (for differential skills) and responsibility (for preferences for labor), when labor supply is along the extensive margin. The criteria from the social choice literature perform better in this regard than the traditional criteria, both in first and second best. More importantly, these equality of opportunity criteria push the second best policy away from an Earned Income Tax Credit and in the direction of a Negative Income tax.optimal income taxation, equality of opportunity, heterogeneous preferences for labor

Bi-connexité, k-connexité et multipoints relais

National audienceLes multipoints relais ont été introduits pour optimiser l'inondation dans un réseau ad hoc. Ils servent aussi, dans le protocole OLSR, à déterminer une sous-topologie qui conserve les plus courts chemin. Nous montrons, comment une généralisation des multipoints relais permet d'obtenir une sous-topologie conservant des propriétés de bi-connexité et plus généralement de k-connexité. Nous montrons de plus, que cette structure de multipoints relais est intrinsèque à toute sous-topologie montrant les mêmes propriétés

Remote spanners: what to know beyond neighbors

International audienceMotivated by the fact that neighbors are generally known in practical routing algorithms, we introduce the notion of remote-spanner. Given an unweighted graph $G$, a sub-graph $H$ with vertex set $V(H)=V(G)$ is an \emph{(\a,\b)-remote-spanner} if for each pair of points $u$ and $v$ the distance between $u$ and $v$ in $H_u$, the graph $H$ augmented by all the edges between $u$ and its neighbors in $G$, is at most \a times the distance between $u$ and $v$ in $G$ plus \b. We extend this definition to $k$-connected graphs by considering minimum length sum over $k$ disjoint paths as distance. We then say that an (\a,\b)-remote-spanner is \emph{$k$-connecting }. In this paper, we give distributed algorithms for computing (1+\eps,1-2\eps)-remote-spanners for any \eps>0, $k$-connecting $(1,0)$-remote-spanners for any $k\ge 1$ (yielding $(1,0)$-remote-spanners for $k=1$) and $2$-connecting $(2,-1)$-remote-spanners. All these algorithms run in constant time for any unweighted input graph. The number of edges obtained for $k$-connecting $(1,0)$-remote-spanner is within a logarithmic factor from optimal (compared to the best $k$-connecting $(1,0)$-remote-spanner of the input graph). Interestingly, sparse $(1,0)$-remote-spanners (i.e. preserving exact distances) with $O(n^4/3)$ edges exist in random unit disk graphs. The number of edges obtained for (1+\eps,1-2\eps)-remote-spanners and $2$-connecting $(2,-1)$-remote-spanners is linear if the input graph is the unit ball graph of a doubling metric (distances between nodes are unknown). Our methodology consists in characterizing remote-spanners as sub-graphs containing the union of small depth tree sub-graphs dominating nearby nodes. This leads to simple local distributed algorithms

Overhead in Mobile Ad-hoc Network Protocols

The present note proposes a survey of protocol overheads in mobile ad-hoc networks. An analysis is proposed to estimate overhead due to control packets. An analysis and simulations are proposed to estimate overhead due to non-optimality of the routes constructed by some protocols

Bi-connectivity, k-connectivity and Multipoint Relays

Multipoint relays were introduced to optimize flooding in ad hoc networks. They are also used to determine a sub-topology containing shortest paths in the OLSR routing protocol. We show that a generalized version of multipoint relays can be used to construct a sub-topology preserving bi-connectivity and more generally $k$-connectivity. Moreover, we show that the multipoint relay structure is intrinsic to any sub-topology with similar properties

Average Size of Unstretched Remote-Spanners

International audienceMotivated by the optimization of link state routing in ad hoc networks, and the concept of multipoint relays, we introduce the notion of remote-spanner. Given an unweighted graph $G$, a remote spanner is a set of links $H$ such that for any pair of nodes $(u,v)$ there exists a shortest path in $G$ for which all links in the path that are not adjacent to $u$ belong to $H$. The remote spanner is a kind of minimal topology information beyond its neighborhood that any node would need in order to compute its shortest paths in a distributed way. This can be extended to $k$-connected graphs by considering minimum length sum over $k$ disjoint paths as distance. In this paper, we give distributed algorithms for computing remote-spanners in order to obtain sparse remote-spanners with various properties. We provide a polynomial distributed algorithm that computes a $k$-connecting unstretched remote-spanner whose number of edges is at a factor $2(1+\log \Delta)$ from optimal where $\Delta$ is the maximum degree of a node. Interestingly, its expected compression ratio in number of edges is O(\frackn\log n) in Erdös-Rényi graph model and O((\frackn)^\frac23) in the unit disk graph model with a uniform Poisson distribution of nodes

Computing connected dominated sets with multipoint relays

Multipoint relays offer an optimized way of flooding packets in a radio network. However, this technique requires the last hop knowledge: to decide wether or not a flooding packet is retransmitted, a node needs to know from which node the packet was received. When considering broadcasting at IP level, this information may be difficult to obtain. We thus propose a scheme for computing an optimized connected dominating set from multipoint relays. This set allows to efficiently broadcast packets without the last hop information with performances close to multipoint relay flooding

Computing connected dominated sets with multipoint relays

International audienceMultipoint relays offer an optimized way of flooding packets in a radio network. However, this technique requires the last hop knowledge: to decide whether or not a flooding packet is retransmitted, a node needs to know from which node the packet was received. When considering broadcasting at IP level, this information may be difficult to obtain. We thus propose a scheme for computing an optimized connected dominating set from multipoint relays. Proof of correctness and simulations are given for all these broadcasting mechanisms

Ad hoc routing protocols with multipoint relaying

National audienceMultipoint relays have been introduced in the proactive protocol OLSR in order to optimize the flooding overhead of control traffic. In this paper we show that multipoint relaying can be used as well in reactive protocols in order to save overhead in route discovery. To this end we specify a very simple reactive protocol called MPRDV (Multipoint Relay Distance Vector protocol). In MPRDV route requests and route replies are all flooded via Multipoint Relays (MPR). They both open routes to their originators. Route repairs are performed by new route request flooding. We show with simulation that the use of MPR flooding does not lead to the control traffic explosion that we experience with basic reactive protocol in presence of frequent route discovery and failure. MPR provide also another optimization since it tends to offer optimal routes to data packets and so increases the protocol performances

Ad hoc communication between intelligent vehicles

International audienceWireless ad hoc networks are composed of mobile autonomous nodes, and can work without any fiwed infrastructure or centralised entity. Moreover, they are adaptive and self-configurating. These kind of networks are well suited for inter-vehicles communication and information exchange (used for tele-traffic management for example). Depending on the context, some of these information need to be sent to almost all the network, and other information need to be sent to a smaller subset of vehicles