 Award ID(s):
 1910149
 Publication Date:
 NSFPAR ID:
 10348209
 Journal Name:
 Proceedings of the 2022 ACMSIAM Symposium on Discrete Algorithms
 Page Range or eLocationID:
 1531  1555
 Sponsoring Org:
 National Science Foundation
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In recent years several compressed indexes based on variants of the BurrowsWheeler transformation have been introduced. Some of these are used to index structures far more complex than a single string, as was originally done with the FMindex [Ferragina and Manzini, J. ACM 2005]. As such, there has been an increasing effort to better understand under which conditions such an indexing scheme is possible. This has led to the introduction of Wheeler graphs [Gagie et al., Theor. Comput. Sci., 2017]. Gagie et al. showed that de Bruijn graphs, generalized compressed suffix arrays, and several other BWT related structures can be represented as Wheeler graphs and that Wheeler graphs can be indexed in a way which is spaceefficient. Hence, being able to recognize whether a given graph is a Wheeler graph, or being able to approximate a given graph by a Wheeler graph, could have numerous applications in indexing. Here we resolve the open question of whether there exists an efficient algorithm for recognizing if a given graph is a Wheeler graph. We present  The problem of recognizing whether a given graph G=(V,E) is a Wheeler graph is NPcomplete for any edge label alphabet of size sigma >= 2, evenmore »

Abstract We present a proof of concept for a spectrally selective thermal midIR source based on nanopatterned graphene (NPG) with a typical mobility of CVDgrown graphene (up to 3000
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We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph G(A cup B,E) with edge weights of 0 or 1. Let w <= n be an upper bound on the weight of any matching in G. Consider the subgraph induced by all the edges of G with a weight 0. Suppose every connected component in this subgraph has O(r) vertices and O(mr/n) edges. We present an algorithm to compute a maximum cardinality matching in G in O~(m(sqrt{w} + sqrt{r} + wr/n)) time. When all the edge weights are 1 (symmetrically when all weights are 0), our algorithm will be identical to the wellknown HopcroftKarp (HK) algorithm, which runs in O(m sqrt{n}) time. However, if we can carefully assign weights of 0 and 1 on its edges such that both w and r are sublinear in n and wr=O(n^{gamma}) for gamma < 3/2, then we can compute maximum cardinality matching in G in o(m sqrt{n}) time. Using our algorithm, we obtain a new O~(n^{4/3}/epsilon^4) time algorithm to compute an epsilonapproximate bottleneck matching of A,B subsetR^2 and an 1/(epsilon^{O(d)}}n^{1+(d1)/(2d1)}) poly logmore »

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