40 research outputs found
Progress on pricing with peering
This paper examines a simple model of how a
provider ISP charges customer ISPs by assuming the provider
ISP wants to maximize its revenue when customer ISPs have
the possibility of setting up peering connections. It is shown that
finding the optimal pricing is NP-complete, and APX-complete.
Customers can respond to price in many ways, including throttling
traffic as well as peering. An algorithm is studied which
obtains a 1/4 approximation for a wide range of customer
responses
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
On maximizing clique, clique-Helly and hereditary clique-Helly induced subgraphs
Clique-Helly and hereditary clique-Helly graphs are polynomial-time recognizable. Recently, we presented a proof that the clique graph recognition problem is NP-complete [L. AlcĆ³n, L. Faria, C.M.H. de Figueiredo, M. Gutierrez, Clique graph recognition is NP-complete, in: Proc. WG 2006, in: Lecture Notes in Comput. Sci., vol. 4271, Springer, 2006, pp. 269-277]. In this work, we consider the decision problems: given a graph G = (V, E) and an integer k ā„ 0, we ask whether there exists a subset V ā² ā V with | V ā² | ā„ k such that the induced subgraph G [V ā² ] of G is, variously, a clique, clique-Helly or hereditary clique-Helly graph. The first problem is clearly NP-complete, from the above reference; we prove that the other two decision problems mentioned are NP-complete, even for maximum degree 6 planar graphs. We consider the corresponding maximization problems of finding a maximum induced subgraph that is, respectively, clique, clique-Helly or hereditary clique-Helly. We show that these problems are Max SNP-hard, even for maximum degree 6 graphs. We show a general polynomial-time frac(1, Ī + 1)-approximation algorithm for these problems when restricted to graphs with fixed maximum degree Ī. We generalize these results to other graph classes. We exhibit a polynomial 6-approximation algorithm to minimize the number of vertices to be removed in order to obtain a hereditary clique-Helly subgraph.Facultad de Ciencias Exacta
On maximizing clique, clique-Helly and hereditary clique-Helly induced subgraphs
Clique-Helly and hereditary clique-Helly graphs are polynomial-time recognizable. Recently, we presented a proof that the clique graph recognition problem is NP-complete [L. AlcĆ³n, L. Faria, C.M.H. de Figueiredo, M. Gutierrez, Clique graph recognition is NP-complete, in: Proc. WG 2006, in: Lecture Notes in Comput. Sci., vol. 4271, Springer, 2006, pp. 269-277]. In this work, we consider the decision problems: given a graph G = (V, E) and an integer k ā„ 0, we ask whether there exists a subset V ā² ā V with | V ā² | ā„ k such that the induced subgraph G [V ā² ] of G is, variously, a clique, clique-Helly or hereditary clique-Helly graph. The first problem is clearly NP-complete, from the above reference; we prove that the other two decision problems mentioned are NP-complete, even for maximum degree 6 planar graphs. We consider the corresponding maximization problems of finding a maximum induced subgraph that is, respectively, clique, clique-Helly or hereditary clique-Helly. We show that these problems are Max SNP-hard, even for maximum degree 6 graphs. We show a general polynomial-time frac(1, Ī + 1)-approximation algorithm for these problems when restricted to graphs with fixed maximum degree Ī. We generalize these results to other graph classes. We exhibit a polynomial 6-approximation algorithm to minimize the number of vertices to be removed in order to obtain a hereditary clique-Helly subgraph.Facultad de Ciencias Exacta