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Approximability of identifying codes and locatingdominating codes
 Information Processing Letters
, 2007
"... We study the approximability and inapproximability of finding identifying codes and locatingdominating codes of the minimum size. In general graphs, we show that it is possible to approximate both problems within a logarithmic factor, but sublogarithmic approximation ratios are intractable. In boun ..."
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We study the approximability and inapproximability of finding identifying codes and locatingdominating codes of the minimum size. In general graphs, we show that it is possible to approximate both problems within a logarithmic factor, but sublogarithmic approximation ratios are intractable. In boundeddegree graphs, there is a trivial constantfactor approximation algorithm, but arbitrarily low approximation ratios remain intractable. In socalled local graphs, there is a polynomialtime approximation scheme. We also consider fractional packing of codes and a related problem of finding minimumweight codes.
On the size of identifying codes in binary hypercubes
, 2008
"... In this paper, we consider identifying codes in binary Hamming spaces F n, i.e., in binary hypercubes. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with several possible applications, for example, to se ..."
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Cited by 4 (0 self)
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In this paper, we consider identifying codes in binary Hamming spaces F n, i.e., in binary hypercubes. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. Currently, the subject forms a topic of its own with several possible applications, for example, to sensor networks. Let C ⊆ F n. For any X ⊆ F n, denote by Ir(X) = Ir(C; X) the set of elements of C within distance r from at least one x ∈ X. Now C ⊆ F n is called an (r, ≤ ℓ)identifying code if the sets Ir(X) are distinct for all X ⊆ F n of size at most ℓ. Let us denote by M (≤ℓ) r (n) the smallest possible cardinality of an (r, ≤ ℓ)identifying code. In [14], it is shown for ℓ = 1 that 1 lim n→∞ n log (≤ℓ) 2 M r (n) = 1 − h(ρ) where r = ⌊ρn⌋, ρ ∈ [0, 1) and h(x) is the binary entropy function. In this paper, we prove that this result holds for any fixed ℓ ≥ 1 when ρ ∈ [0, 1/2). We also show that M (≤ℓ) r (n) = O(n 3/2) for every fixed ℓ and r slightly less than n/2, and give an explicit construction of small (r, ≤ 2)identifying codes for r = ⌊n/2 ⌋ − 1.
The dIdentifying Codes Problem for Vertex Identification in Graphs: Probablistic Analysis and an Approximation Algorithm
 In COCOON 2006 (12th Annual International Computing and Combinatorics Conference
, 2006
"... algorithm Proofs omitted due to space constraints are put into the appendix. ..."
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Cited by 1 (1 self)
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algorithm Proofs omitted due to space constraints are put into the appendix.