Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

An efficient closed frequent itemset miner for the MOA stream mining system

Mining itemsets is a central task in data mining, both in the batch and the streaming paradigms. While robust, efficient, and well-tested implementations exist for batch mining, hardly any publicly available equivalent exists for the streaming scenario. The lack of an efficient, usable tool for the task hinders its use by practitioners and makes it difficult to assess new research in the area. To alleviate this situation, we review the algorithms described in the literature, and implement and evaluate the IncMine algorithm by Cheng, Ke, and Ng (2008) for mining frequent closed itemsets from data streams. Our implementation works on top of the MOA (Massive Online Analysis) stream mining framework to ease its use and integration with other stream mining tasks. We provide a PAC-style rigorous analysis of the quality of the output of IncMine as a function of its parameters; this type of analysis is rare in pattern mining algorithms. As a by-product, the analysis shows how one of the user-provided parameters in the original description can be removed entirely while retaining the performance guarantees. Finally, we experimentally confirm both on synthetic and real data the excellent performance of the algorithm, as reported in the original paper, and its ability to handle concept drift.Postprint (published version

Destination-based Routing and Circuit Allocation for Future Traffic Growth

Internet traffic continues to grow relentlessly, driven largely by increasingly high- \\ resolution video streaming, the increasing adoption of cloud computing, the emergence of 5G networks, and the ever-growing reach of social media and social networks. Existing networks use packet switching to route packets on a hop-by-hop basis from the source to the destination. However, they suffer from two shortcomings. First, in existing networks, packets are routed along a fixed shortest path using the Open Shortest Path First (OSPF) protocol or obliviously load-balanced across equal-cost paths using the Equal-Cost Multi-Path (ECMP) protocol. These routing protocols do not fully utilize the network capacity because they do not adapt to network congestions in their routing decisions. Second, although studies have shown that the majority of packets processed by Internet routers are pass-through traffic, packets nonetheless have to be queued and routed at every hop in existing networks, which unnecessarily adds substantial delays and processing costs.In this thesis, we present two new approaches to overcome these shortcomings. First, we propose new backpressure-based routing algorithms which use only shortest-path routes when they are sufficient to accommodate the given traffic load, but will incrementally expand routing choices as needed to accommodate increasing traffic loads. This avoids the poor delay performance inherent in backpressure-based routing algorithms where packets may take long detours under light or moderate loads, and still retains the notable advantage, the network-wide optimal throughput, because packets are adaptively routed along less congested paths.Second, we propose a unified packet and circuit switched network in which the underlying optical transport is used to circuit-switch pass-through traffic by means of pre-established circuits. This avoids unnecessary packet queuing delays and processing costs at each hop. We propose a novel convex optimization framework based on a new destination-based multicommodity flow formulation for the allocation of circuits in such unified networks

Variations on Memetic Algorithms for Graph Coloring Problems

11 pages, 8 figures, 3 tables, 2 algorithmsInternational audienceGraph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for

Coding Theory

Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances