In this paper we show that series-parallel graphs (i.e., K 4-minor free graphs) can be represented as contact intersection graphs of straight-line segments in three directions. Moreover, in our representations no two ...
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ISBN:
(纸本)1860948278
In this paper we show that series-parallel graphs (i.e., K 4-minor free graphs) can be represented as contact intersection graphs of straight-line segments in three directions. Moreover, in our representations no two segments of the same direction intersect.
If robots are deployed in large numbers in disaster scenarios, the ability to discover and exchange resources and services with other robots in an open, heterogeneous, large-scale network will be essential for a succe...
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If robots are deployed in large numbers in disaster scenarios, the ability to discover and exchange resources and services with other robots in an open, heterogeneous, large-scale network would be essential for a succ...
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If robots are deployed in large numbers in disaster scenarios, the ability to discover and exchange resources and services with other robots in an open, heterogeneous, large-scale network would be essential for a successful operation. In this paper we present a discovery protocol that enables robots to efficiently locate resources and services available in large-scale networks. It is specifically designed for robot networks which are characterized by potentially highly dynamic network topologies and high service announcement-to-lookup ratios. The protocol exploits the position data of the robots to increase scalability and efficiency. A cell-based overlay structure is created, with master nodes in each cell. Through proactive intra-cell communication and reactive inter-cell communication, scalability is ensured and the effects of node movements on the overall network are minimized.
作者：
STEMMER, WPCPalo Alto Institute of Molecular Medicine 2462 Wyandotte Street Mountain View
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Using recombination to search more efficiently and thoroughly instead of making bigger combinatorial libraries
Using recombination to search more efficiently and thoroughly instead of making bigger combinatorial libraries
We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets \(\sigma,\rho\) of non-negative integers, a \((\sigma,\rho)\)-set of a graph \(G\) i...
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We investigate how efficiently a well-studied family of domination-type problems can be solved on bounded-treewidth graphs. For sets \(\sigma,\rho\) of non-negative integers, a \((\sigma,\rho)\)-set of a graph \(G\) is a set \(S\) of vertices such that \(|N(u)\cap S|\in\sigma\) for every \(u\in S\), and \(|N(v)\cap S|\in\rho\) for every \(v\not\in S\). The problem of finding a \((\sigma,\rho)\)-set (of a certain size) unifies standard problems such as Independent Set, Dominating Set, Independent Dominating Set, and many *** all pairs of finite or cofinite sets \((\sigma,\rho)\), we determine (under standard complexity assumptions) the best possible value \(c_{\sigma,\rho}\) such that there is an algorithm that counts \((\sigma,\rho)\)-sets in time \(c_{\sigma,\rho}^{\rm{tw}} \cdot n^{O(1)}\) (if a tree decomposition of width \(\rm{tw}\) is given in the input). Let \(s_{\rm{top}}\) denote the largest element of \(\sigma\) if \(\sigma\) is finite, or the largest missing integer \(+1\) if \(\sigma\) is cofinite; \(r_{\rm{top}}\) is defined analogously for \(\rho\). Surprisingly, \(c_{\sigma,\rho}\) is often significantly smaller than the natural bound \(s_{\rm{top}}+r_{\rm{top}}+2\) achieved by existing algorithms [van Rooij, 2020]. Toward defining \(c_{\sigma,\rho}\), we say that \((\sigma,\rho)\) is m-structured if there is a pair \((\alpha,\beta)\) such that every integer in \(\sigma\) equals \(\alpha\) mod m, and every integer in \(\rho\) equals \(\beta\) mod m. Then, setting—\(c_{\sigma,\rho}=s_{\rm{top}}+r_{\rm{top}}+2\) if \((\sigma,\rho)\) is not m-structured for any \(\rm{m}\geq 2\),—\(c_{\sigma,\rho}=\max\{s_{\rm{top}},r_{\rm{top}}\}+2\) if \((\sigma,\rho)\) is 2-structured, but not \(\rm{m}\)-structured for any \(\rm{m}\geq 3\), and \(s_{\rm{top}}=r_{\rm{top}}\) is even, and—\(c_{\sigma,\rho}=\max\{s_{\rm{top}},r_{\rm{top}}\}+1\), otherwise,we provide algorithms counting \((\sigma,\rho)\)-sets in time \(c_{\sigma,\rho}^{\rm{tw}}\cdot n^{O(1)}\). For e
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, suc...
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Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition’s width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms that achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width *** by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth. Here, shrubdepth is a bounded-depth analogue of cliquewidth, in the same way as treedepth is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. More precisely, we prove that on n-vertex graphs equipped with a tree-model (a decomposition notion underlying shrubdepth) of depth d and using k labels,•Independent Set and Dominating Set can be solved in time \(2^{\mathcal {O}(dk)}\cdot n^{\mathcal {O}(1)}\) using \(\mathcal {O}(dk\log n)\) space;•Max Cut can be solved in time \(n^{\mathcal {O}(dk)}\) using \(\mathcal {O}(dk\log n)\) *** also establish a lower bound, conditional on a certain assumption about the complexity of Longest Common Subsequence, which shows that at least in the case of Independent Set the exponent of the parametric factor in the time complexity has to grow with d if one wishes to keep the space complexity polynomial.
For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets σ, ρ of non-negative integers, a (σ, ρ)-set of a graph ...
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For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets σ, ρ of non-negative integers, a (σ, ρ)-set of a graph G is a set S of vertices such that |N(u)∩S| ∈ σ for every u ∈ S, and |N(v)∩S| ∈ ρ for every \(v\not\in S\). The problem of finding a (σ, ρ)-set (of a certain size) unifies common problems like Independent Set, Dominating Set, Independent Dominating Set, and many *** an accompanying paper, it is proven that, for all pairs of finite or cofinite sets (σ, ρ), there is an algorithm that counts (σ, ρ)-sets in time \((c_{\sigma,\rho })^{\sf tw}\cdot n^{{\rm O}(1)}\) (if a tree decomposition of width \({\sf tw}\) is given in the input). Here, cσ, ρ is a constant with an intricate dependency on σ and ρ. Despite this intricacy, we show that the algorithms in the accompanying paper are most likely optimal, i.e., for any pair (σ, ρ) of finite or cofinite sets where the problem is non-trivial, and any ε > 0, a \((c_{\sigma,\rho }-\varepsilon)^{\sf tw}\cdot n^{{\rm O}(1)}\)-algorithm counting the number of (σ, ρ)-sets would violate the Counting Strong Exponential-Time Hypothesis (#SETH). For finite sets σ and ρ, our lower bounds also extend to the decision version, showing that those algorithms are optimal in this setting as well.
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