Antoine Musitelli’s research while affiliated with University of Padua and other places

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Publications (6)


On matrices with the Edmonds–Johnson property arising from bidirected graphs
  • Article

October 2017

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23 Reads

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1 Citation

Journal of Combinatorial Theory Series B

Alberto Del Pia

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Antoine Musitelli

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Giacomo Zambelli

In this paper we study totally half-modular matrices obtained from (0,±1)-matrices with at most two nonzero entries per column by multiplying by 2 some of the columns. We give an excluded-minor characterization of the matrices in this class having strong Chvàtal rank 1. Our result is a special case of a conjecture by Gerards and Schrijver It also extends a well known theorem of Edmonds and Johnson


Competitive ratio of List Scheduling on uniform machines and randomized heuristics

February 2011

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33 Reads

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7 Citations

Journal of Scheduling

We study online scheduling on m uniform machines, where m−1 of them have a reference speed 1 and the last one a speed s with 0≤s≤1. The competitive ratio of the well-known List Scheduling (LS) algorithm is determined. For some values of s and m=3, LS is proven to be the best deterministic algorithm. We describe a randomized heuristic for m machines. Finally, for the case m=3, we develop and analyze the competitive ratio of a randomized algorithm which outperforms LS for any s.


Recognizing binet matrices

July 2010

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15 Reads

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6 Citations

Mathematical Programming

Binet matrices generalize network matrices and play an important role in combinatorial optimization. A first polynomial-time algorithm for recognizing binet matrices appeared in the author’s doctoral thesis. In this paper, we present some key ideas and results involved in the design of this algorithm. We show how we can find a Camion basis of the input matrix, whenever this one is binet, and then reduce the recognition problem to that of special binet matrices called bicyclic and cyclic.


Recognition of generalized network matrices

August 2008

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157 Reads

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7 Citations

In this thesis, we deal with binet matrices, an extension of network matrices. The main result of this thesis is the following. A rational matrix A of size n×m can be tested for being binet in time O(n6m). If A is binet, our algorithm outputs a nonsingular matrix B and a matrix N such that [B N] is the node-edge incidence matrix of a bidirected graph (of full row rank) and A = B-1N. Furthermore, we provide some results about Camion bases. For a matrix M of size n × m', we present a new characterization of Camion bases of M, whenever M is the node-edge incidence matrix of a connected digraph (with one row removed). Then, a general characterization of Camion bases as well as a recognition procedure which runs in O(n2m') are given. An algorithm which finds a Camion basis is also presented. For totally unimodular matrices, it is proven to run in time O((nm)2) where m = m' – n. The last result concerns specific network matrices. We give a characterization of nonnegative {ε, ρ}-noncorelated network matrices, where ε and ρ are two given row indexes. It also results a polynomial recognition algorithm for these matrices.


New polynomial-time algorithms for Camion bases

December 2006

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10 Reads

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2 Citations

Discrete Mathematics

Let M be a finite set of vectors in Rn of cardinality m and H(M)={{x∈Rn:cTx=0}:c∈M} the central hyperplane arrangement represented by M. An independent subset of M of cardinality n is called a Camion basis, if it determines a simplex region in the arrangement H(M). In this paper, we first present a new characterization of Camion bases, in the case where M is the column set of the node-edge incidence matrix (without one row) of a given connected digraph. Then, a general characterization of Camion bases as well as a recognition procedure which runs in O(n2m) are given. Finally, an algorithm which finds a Camion basis is presented. For certain classes of matrices, including totally unimodular matrices, it is proven to run in polynomial time and faster than the algorithm due to Fonlupt and Raco.


Citations (3)


... Binet matrices are 2-regular and a generalization of network matrices. The main result in [20] is a polynomial-time algorithm for the recognition of binet matrices and thus for the recognition of a subclass of 2-regular matrices. ...

Reference:

Exact Decomposition Branching exploiting Lattice Structures
Recognizing binet matrices
  • Citing Article
  • July 2010

Mathematical Programming

... They prove that LS has a competitive ratio of = 1+ √ 5 2 ≈ 1.618 for the case = 2, and the ratio is at most 1 + √︀ ( − 1)/2 for ≥ 3. This bound is proved tight for 3 ≤ ≤ 6. Musitelli and Nicoletti [34] consider the case where − 1 machines are of speed 1 and the last machine is of speed (0 ≤ ≤ 1). They first prove that LS is the best deterministic algorithm for some specific values of and = 3. ...

Competitive ratio of List Scheduling on uniform machines and randomized heuristics
  • Citing Article
  • February 2011

Journal of Scheduling

... [7,9,10,23,29,43,[46][47][48]), there are no efficient methods that test whether a matrix is binet or not. A polynomial time algorithm has been published in [30,31]. However, the approach presented in these works is overly complicated, and concerns have been raised (see [27]) regarding the binet representation produced as output by the mentioned algorithm when the input matrix is proven to be binet. ...

Recognition of generalized network matrices
  • Citing Article
  • August 2008