Network correlated data gathering with explicit communication: NP-completeness and algorithms

We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal

Routing Games over Time with FIFO policy

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201

The complexity of the characterization of networks supporting shortest-path interval routing

AbstractInterval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been thoroughly investigated for each of the variants and under different models, with only partial answers, both positive and negative, given so far. In this paper, we study the characterization problem under the most basic model (the one unit cost), and with the most restrictive memory requirements (one interval per edge). We prove that this problem is NP-hard (even for the restricted class of graphs of diameter at most 3). Our result holds for all variants of Interval Routing. It significantly extends some related NP-hardness result, and implies that, unless P=NP, partial characterization results of some classes of networks which support shortest path Interval Routing, cannot be pushed further to lead to efficient characterizations for these classes

Shortest paths between shortest paths and independent sets

We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even when we know that the sequence has polynomial length. Moreover, we also study reconfiguration of independent sets in three different models and analyze relationships between these models, observing that shortest path reconfiguration is a special case of independent set reconfiguration in perfect graphs, under any of the three models. Finally, we give polynomial results for restricted classes of graphs (even-hole-free and $P_4$-free graphs)

Path computation in multi-layer networks: Complexity and algorithms

Carrier-grade networks comprise several layers where different protocols coexist. Nowadays, most of these networks have different control planes to manage routing on different layers, leading to a suboptimal use of the network resources and additional operational costs. However, some routers are able to encapsulate, decapsulate and convert protocols and act as a liaison between these layers. A unified control plane would be useful to optimize the use of the network resources and automate the routing configurations. Software-Defined Networking (SDN) based architectures, such as OpenFlow, offer a chance to design such a control plane. One of the most important problems to deal with in this design is the path computation process. Classical path computation algorithms cannot resolve the problem as they do not take into account encapsulations and conversions of protocols. In this paper, we propose algorithms to solve this problem and study several cases: Path computation without bandwidth constraint, under bandwidth constraint and under other Quality of Service constraints. We study the complexity and the scalability of our algorithms and evaluate their performances on real topologies. The results show that they outperform the previous ones proposed in the literature.Comment: IEEE INFOCOM 2016, Apr 2016, San Francisco, United States. To be published in IEEE INFOCOM 2016, \<http://infocom2016.ieee-infocom.org/\&g

Optimizing IGP Link Costs for Improving IP-level Resilience

Recently, major vendors have introduced new router platforms to the market that support fast IP-level failure pro- tection out of the box. The implementations are based on the IP Fast ReRoute–Loop Free Alternates (LFA) standard. LFA is simple, unobtrusive, and easily deployable. This simplicity, however, comes at a severe price, in that LFA usually cannot protect all possible failure scenarios. In this paper, we give new graph theoretical tools for analyzing LFA failure case coverage and we seek ways for improvement. In particular, we investigate how to optimize IGP link costs to maximize the number of protected failure scenarios, we show that this problem is NP- complete even in a very restricted formulation, and we give exact and approximate algorithms to solve it. Our simulation studies show that a deliberate selection of IGP costs can bring many networks close to complete LFA-based protection

An FPT Algorithm for Minimum Additive Spanner Problem

For a positive integer t and a graph G, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. The Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners, the Minimum Additive t-Spanner Problem is hard to handle and hence only few results are known for it. In this paper, we study the Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter, and give a fixed-parameter algorithm for it. We also extend our result to the case with both a multiplicative approximation factor ? and an additive approximation parameter ?, which we call (?, ?)-spanners