The syntax and semantics of a domain-specific language for flow-network design

Kfoury, A. J.

doi:10.1016/j.scico.2012.12.009

Cited by 5 publications

(14 citation statements)

References 23 publications

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“…. , X r+s+t with X = X r+s+t , which is listed in order of increasing consecutive levels and divided into three groups: 8 • {X 1 , . .…”

Section: Proof Of Correctness and Complexitymentioning

confidence: 99%

“…If innermost-cycle(ϕ) = X, it does not necessarily follow that ϕ ∈ M , unless ϕ's clockwise neighbor is in M -as asserted here 8. In general, 0 r 1, while s and t can be arbitrarily large integers 0.…”

mentioning

confidence: 92%

“…Background and Motivation. Besides questions of optimization and the variations which it naturally suggests, graph reassembling is an abstraction of an operation carried out by programs in a domain-specific language for the design of flow networks [2,7,8,14]. In network reassembling, the network is taken apart and reassembled in an order determined by the designer.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Efficient reassembling of three-regular planar graphs

Kfoury

Sisson

2020

J Comb Optim

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A reassembling of a simple graph G = (V, E) is an abstraction of a problem arising in earlier studies of network analysis [2,7,8,14]. There are several equivalent definitions of graph reassembling; in this report we use a definition which makes it closest to the notion of graph carving. A reassembling is a rooted binary tree whose nodes are subsets of V and whose leaf nodes are singleton sets, with each of the latter containing a distinct vertex of G. The parent of two nodes in the reassembling is the union of the two children's vertex sets. The root node of the reassembling is the full set V . The edge-boundary degree of a node in the reassembling is the number of edges in G that connect vertices in the node's set to vertices not in the node's set. A reassembling's α-measure is the largest edge-boundary degree of any node in the reassembling. A reassembling of G is α-optimal if its α-measure is the minimum among all α-measures of G's reassemblings.The problem of finding an α-optimal reassembling of a simple graph in general was already shown to be NP-hard [10, 11, among others].In this report we present an algorithm which, given a 3-regular plane graph G = (V, E) as input, returns a reassembling of G with an α-measure independent of n = | V | and upper-bounded by 2k, where k is the edge-outerplanarity of G. (Edge-outerplanarity is distinct but closely related to the usual notion of outerplanarity; as with outerplanarity, for a fixed edge-outerplanarity k, the number n of vertices can be arbitrarily large.) Our algorithm runs in linear time O(n). Moreover, we construct a class of 3-regular plane graphs for which this α-measure is optimal, by proving that 2k is the lower bound on the α-measure of any reassembling of a graph in that class.

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“…. , X r+s+t with X = X r+s+t , which is listed in order of increasing consecutive levels and divided into three groups: 8 • {X 1 , . .…”

Section: Proof Of Correctness and Complexitymentioning

confidence: 99%

mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Efficient reassembling of three-regular planar graphs

Kfoury

Sisson

2020

J Comb Optim

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“…Future work related to graph reassembling (and specifically related to the balanced case) includes a study of classes of graphs for which α-optimization and/or β-optimization of their reassembling can be carried out in low-degree polynomial times. On the other hand, as indicated in our earlier report [15], the smaller the α and β measures are, the more efficient the execution of programs is, in a domain-specific language (DSL) for the design of flow networks [5,13,20,14]. Beinstock in [6] presents some elementary classes of graphs with small optimal tree congestion as well as an upper bound for the value of optimal tree congestion based on the tree decomposition of the graphs.…”

Section: Related and Future Workmentioning

confidence: 99%

Efficient Reassembling of Graphs, Part 2: The Balanced Case

Mirzaei,

Kfoury

2016

Preprint

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The reassembling of a simple connected graph G = (V, E) with n = V ⩾ 1 vertices is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to a binary tree B -its so-called reassembling tree, with root node at the top and n leaf nodes at the bottom -where every cross-section corresponds to a partition of V (a block in the partition is a node in the cross-section) such that:• the bottom (or first) cross-section (i.e., all the leaves) is the finest partition of V with n one-vertex blocks, • the top (or last) cross-section (i.e., the root) is the coarsest partition with a single block, the entire set V , • a node (or block) in an intermediate cross-section (or partition) is the result of merging its two children nodes (or blocks) in the cross-section (or partition) below it.The edge-boundary degree of a block A of vertices is the number of edges with one endpoint in A and one endpoint in (V − A). The maximum edge-boundary degree encountered during the reassembling process is what we call the α-measure of the reassembling, and the sum of all edge-boundary degrees is its β-measure.The α-optimization (resp. β-optimization) of the reassembling of G is to determine a reassembling tree B that minimizes its α-measure (resp. β-measure).There are different forms of reassembling, depending on the shape of the reassembling tree B. In an earlier report, we studied linear reassembling, which is the case when the height of B is (n−1). In this report, we study balanced reassembling, when B has height ⌈log n⌉. In a forthcoming report, we study general reassembling, which is the case when the height of B can be any number between (n − 1) and ⌈log n⌉.The two main results in this report are the NP-hardness of α-optimization and β-optimization of balanced reassembling. The first result is obtained by a sequence of polynomial-time reductions from minimum bisection of graphs (known to be NP-hard), and the second by a sequence of polynomial-time reductions from clique cover of graphs (known to be NP-hard).

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Efficient reassembling of graphs, part 1: the linear case

Kfoury

Mirzaei

2016

J Comb Optim

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The reassembling of a simple connected graph G = (V, E) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps:(1) We cut every edge of G into two halves, thus obtaining a collection of n = | V | one-vertex components, such that for every v ∈ V the one-vertex component {v} has degree(v) half edges attached to it. (2) We splice the two halves of every edge together, not of all the edges at once, but in some ordering of the edges that minimizes two measures that depend on the edge-boundary degrees of assembled components.A component A is a subset of V and its edge-boundary degree is the number of edges in G with one endpoint in A and one endpoint in V − A (which is the same as the number of half edges attached to A after all edges with both endpoints in A have been spliced together). The maximum edge-boundary degree encountered during the reassembling process is what we call the α-measure of the reassembling, and the sum of all edgeboundary degrees is its β-measure. The α-optimization (resp. β-optimization) of the reassembling of G is to determine an order for splicing the edges that minimizes its α-measure (resp. β-measure). There are different forms of reassembling, depending on restrictions and variations on the ordering of the edges. We consider only cases satisfying the condition that if an edge between disjoint components A and B is spliced, then all the edges between A and B are spliced at the same time. In this report, we examine the particular case of linear reassembling, which requires that the next edge to be spliced must be adjacent to an already spliced edge. We delay other forms of reassembling to follow-up reports. We prove that α-optimization of linear reassembling B Saber Mirzaei 123 J Comb Optim and minimum-cutwidth linear arrangment (CutWidth) are polynomially reducible to each other, and that β-optimization of linear reassembling and minimum-cost linear arrangement (MinArr) are polynomially reducible to each other. The known NPhardness of CutWidth and MinArr imply the NP-hardness of α-optimization and β-optimization.

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The syntax and semantics of a domain-specific language for flow-network design

Cited by 5 publications

References 23 publications

Efficient reassembling of three-regular planar graphs

Efficient reassembling of three-regular planar graphs

Efficient Reassembling of Graphs, Part 2: The Balanced Case

Efficient reassembling of graphs, part 1: the linear case

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