Marc-Antoine Weisser

Bin packing with fragmentable items

We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity. We give and prove several properties then we present various approximation algorithms and specially a 6 5 -approximation algorithm.

Bandwidth Optimization for Multicast Transmissions in Virtual Circuit Networks

The CARRIOCAS project aims to guarantee QoS connectivity services to distributed applications in a Telecom carrier network. A large number of these applications (for example video applications) use a multicast service packet delivery. Multicast which minimizes the total used bandwidth in the MPLS network has become an important subject. We study multicast routing in the network where only some routers can duplicate packets. We prove that the construction of a multicast tree minimizing the bandwidth used in such a network is a NP -complete problem and we propose an heuristic algorithm to solve it. We evaluate the performance of the heuristic in terms of total bandwidth used by the multicast for different network sizes.

A Practical Greedy Approximation for the Directed Steiner Tree Problem

The Directed Steiner Tree (DST) NP-hard problem asks, considering a directed weighted graph with \(n\) nodes and \(m\) arcs, a node \(r\) called root and a set of \(k\) nodes \(X\) called terminals, for a minimum cost directed tree rooted at \(r\) spanning \(X\). The best known polynomial approximation ratio for DST is a \(O(k^\varepsilon )\)-approximation greedy algorithm. However, a much faster \(k\)-approximation, returning the shortest paths from \(r\) to \(X\), is generally used in practice. We give in this paper a new \(O(\sqrt{k})\)-approximation greedy algorithm called Greedy\(_\mathrm{FLAC }\) \(^\triangleright \), derived from a new fast \(k\)-approximation algorithm called Greedy\(_\mathrm{FLAC }\) running in time at most \(O(n m k^2)\).

Directed Steiner Tree with Branching Constraint

Given a directed weighted graph G, a root r and k terminals, the k-Directed Steiner Tree problem is to find a minimum cost tree rooted at r and spanning all terminals. If this problem has several applications in multicast routing in packet switching networks, the modeling is not adapted anymore in networks based upon the circuit switching principle in which some nodes, called non diffusing nodes, are not able to duplicate packets. We define a more general problem, named Directed Steiner Tree with Limited number of Diffusing nodes (DSTLD), able to model the multicast in a network containing at most d diffusing nodes. We show that DSTLD is XP with respect to d, and use this result to build a \(\lceil \frac{k-1}{d} \rceil\)-approximation XP in d for DST. Finally, we prove that, under the assumption that NP \(\not\subseteq\) DTIME[n O(loglogn)], there is no polynomial approximation algorithm for DSTLD with ratio \(1+(\frac{1}{e} - \varepsilon) \cdot \frac{k}{d-1}\) for every constant e > 0.

The inter-domain hierarchy in measured and randomly generated AS-level topologies

Independent operator networks are called either Autonomous Systems (AS) or domains. Numerous studies based on complex measurement platforms have been carried out for over ten years now in order to discover the Internet topology on domain level. The routing realized by Border Gateway Protocol (BGP) is strongly influenced by commercial relationships which exist between domains, because domain operators do not want to make public the routes they know, as announcing certain routes would deprive them of a possible financial benefit. Consequently, routes available in BGP tables are valley-free and they are “spanned” on the inter-domain hierarchy. This property of BGP routes has an impact on the performance of protocols which are proposed to assure the QoS. We examined the existing Internet topologies gathered on the domain level over the six year period in the context of their hierarchy. We used aSHIIP, our random hierarchical topology generator, to induct the hierarchy into the collected topologies. We proposed new methods for detecting the core of a network. Thanks to this analysis we have been able to put forward solid inter-domain hierarchy induction methods which are implemented in our publicly available tool.

Directed Steiner trees with diffusion costs

Given a directed arc-weighted graph G with n nodes, a root r and k terminals, the directed steiner tree problem (DST) consists in finding a minimum-weight tree rooted at r and spanning all the terminals. If this problem has several applications in multicast routing in packet switching networks, the modeling is not adapted anymore in networks based upon the circuit switching principle in which some nodes, called non diffusing nodes, are unable to duplicate packets. We define a more general problem, namely the directed steiner tree with a limited number of diffusing nodes (DSTLD), that enables us to model multicast in a network containing at most d diffusing nodes. We show that DSTLD is XP with respect to d, and use this result to build a

The First Approximation Algorithm for the Maximin Latin Hypercube Design Problem

\left\lceil \frac{k-1}{d} \right\rceil

A distributed algorithm for inter-domain resources provisioning

k-1d-approximation algorithm for DST that is XP in d. We deduce from that result a strong inapproximability property. In particular, we prove that, under the assumption that NP