Aristotelis Giannakos

On the complexity of scheduling with large communication delays

Abstract Given a directed acyclic graph (dag) with unit execution time tasks and constant communication delays c ⩾ 2, we are interested in deciding if there is a schedule for the dag of length at most L. We prove that the problem is polynomial when L is equal to (c + 1), or (c + 2) for the special case of c = 2, and that it is NP-complete for (c + 3) for any value of c, even in the case of a bipartite dag of depth one.

Exact and approximation algorithms for densest k-subgraph

The DENSEST k-SUBGRAPH problem is a generalization of the maximum clique problem, in which we are given a graph G and a positive integer k, and we search among the subsets of k vertices of G one inducing a maximum number of edges. In this paper, we present algorithms for finding exact solutions of k-SUBGRAPH improving the trivial exponential time complexity of O *(2 n ) and using polynomial space. Two FPT algorithms are also proposed; the first considers as parameter the treewidth of the input graph and uses exponential space, while the second is parameterized by the size of the minimum vertex cover and uses polynomial space. Finally, we propose several approximation algorithms running in moderately exponential or parameterized time.

A Message-Optimal Sink Mobility Model for Wireless Sensor Networks

The paper proposes an algorithm for collecting data from a wireless sensor network modeled as a random geometric graph in the unit square. The sensors are supposed to work in an asychronous communication mode (they store the measures they perform and transmit a message containing the data, upon receival of a trigger signal). The model assumes a mobile sink passing near the sensors, and asking the sensors to transmit their data. The algorithm defines a route for the sink such that the number of messages that a sensor needs to transmit be as low as possible.We also present a kind of “controled” random walk in a(connected) random geometric graph that is based upon the main idea of the sink routing algorithm, reducing the graph cover time to Θ(n log log n) instead of Θ(n log n) needed when a simple random walk is performed.The model can be generalized for the case of more than one mobile sink, and the algorithm can be modified to deal with locally uniform density of sensors deployed in the field.

On the performance of congestion games for optimum satisfiability problems

We introduce and study a congestion game having MAX SAT as an underlying structure and show that its price of anarchy is 1/2. The main result is a redesign of the game leading to an improved price of anarchy of 2/3 from which we derive a non oblivious local search algorithm for MAX SAT with locality gap 2/3. A similar congestion MIN SAT game is also studied.

An Approximation Algorithm for the Three Depots Hamiltonian Path Problem

In this paper, we propose an approximation algorithm for solving the three depots Hamiltonian path problem (3DHPP). The problem studied can be viewed as a variant of the well-known Hamiltonian path problem with multiple depots (cf., Demange [Mathematiques et Informatique, Gazette, 102 (2004)] and Malik et al. [Oper. Res. Lett. 35, 747–753 (2007)]). For the 3DHPP, we show the existence of a \(\frac{3} {2}\)-approximation algorithm for a broad family of metric cases which also guarantees a ratio r < 2 in the general metric case. The proposed algorithm is mainly based on extending the construction scheme already used by Rathinam et al. [Oper. Res. Lett. 38, 63–68 (2010)]. The aforementioned result is established for a variant of the three-depot problem, that is, when costs are symmetric and satisfy the triangle inequality.

The max quasi-independent set problem

In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, f-QIS, consists of, given a graph and a non-decreasing function f, finding a maximum size subset Q of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to f(|Q|). For this problem, we show an exact solution method that runs within time

Online maximum k-coverage

O^*(2^{\frac{d-27/23}{d+1}n})

Greedy algorithms for on-line set-covering and related problems

on graphs of average degree bounded by d. For the most specifically defined γ-QIS and k-QIS problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.