5,208 research outputs found
Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets
This paper investigates the problem of recovering the support of structured
signals via adaptive compressive sensing. We examine several classes of
structured support sets, and characterize the fundamental limits of accurately
recovering such sets through compressive measurements, while simultaneously
providing adaptive support recovery protocols that perform near optimally for
these classes. We show that by adaptively designing the sensing matrix we can
attain significant performance gains over non-adaptive protocols. These gains
arise from the fact that adaptive sensing can: (i) better mitigate the effects
of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor
Combinatorial specification of permutation classes
This article presents a methodology that automatically derives a
combinatorial specification for the permutation class C = Av(B), given its
basis B of excluded patterns and the set of simple permutations in C, when
these sets are both finite. This is achieved considering both pattern avoidance
and pattern containment constraints in permutations.The obtained specification
yields a system of equations satisfied by the generating function of C, this
system being always positiveand algebraic. It also yields a uniform random
sampler of permutations in C. The method presentedis fully algorithmic
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Hardness of submodular cost allocation : lattice matching and a simplex coloring conjecture
We consider the Minimum Submodular Cost Allocation (MSCA) problem. In this problem, we are given k submodular cost functions f1, ... , fk: 2V -> R+ and the goal is to partition V into k sets A1, ..., Ak so as to minimize the total cost sumi = 1,k fi(Ai). We show that MSCA is inapproximable within any multiplicative factor even in very restricted settings; prior to our work, only Set Cover hardness was known. In light of this negative result, we turn our attention to special cases of the problem. We consider the setting in which each function fi satisfies fi = gi + h, where each gi is monotone submodular and h is (possibly non-monotone) submodular. We give an O(k log |V|) approximation for this problem. We provide some evidence that a factor of k may be necessary, even in the special case of HyperLabel. In particular, we formulate a simplex-coloring conjecture that implies a Unique-Games-hardness of (k - 1 - epsilon) for k-uniform HyperLabel and label set [k]. We provide a proof of the simplex-coloring conjecture for k=3
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