Showing papers on "Path graph published in 2018"
TL;DR: A high performance Chemical Induced Disease relation extraction system is presented and graph kernels are effective in extracting relations that are expressed in multiple sentences, and it is shown that the graph kernels, namely the ASM and APG kernels, substantially outperform the tree kernels.
Abstract: Relation extraction from biomedical publications is an important task in the area of semantic mining of text. Kernel methods for supervised relation extraction are often preferred over manual feature engineering methods, when classifying highly ordered structures such as trees and graphs obtained from syntactic parsing of a sentence. Tree kernels such as the Subset Tree Kernel and Partial Tree Kernel have been shown to be effective for classifying constituency parse trees and basic dependency parse graphs of a sentence. Graph kernels such as the All Path Graph kernel (APG) and Approximate Subgraph Matching (ASM) kernel have been shown to be suitable for classifying general graphs with cycles, such as the enhanced dependency parse graph of a sentence. In this work, we present a high performance Chemical-Induced Disease (CID) relation extraction system. We present a comparative study of kernel methods for the CID task and also extend our study to the Protein-Protein Interaction (PPI) extraction task, an important biomedical relation extraction task. We discuss novel modifications to the ASM kernel to boost its performance and a method to apply graph kernels for extracting relations expressed in multiple sentences. Our system for CID relation extraction attains an F-score of 60%, without using external knowledge sources or task specific heuristic or rules. In comparison, the state of the art Chemical-Disease Relation Extraction system achieves an F-score of 56% using an ensemble of multiple machine learning methods, which is then boosted to 61% with a rule based system employing task specific post processing rules. For the CID task, graph kernels outperform tree kernels substantially, and the best performance is obtained with APG kernel that attains an F-score of 60%, followed by the ASM kernel at 57%. The performance difference between the ASM and APG kernels for CID sentence level relation extraction is not significant. In our evaluation of ASM for the PPI task, ASM performed better than APG kernel for the BioInfer dataset, in the Area Under Curve (AUC) measure (74% vs 69%). However, for all the other PPI datasets, namely AIMed, HPRD50, IEPA and LLL, ASM is substantially outperformed by the APG kernel in F-score and AUC measures. We demonstrate a high performance Chemical Induced Disease relation extraction, without employing external knowledge sources or task specific heuristics. Our work shows that graph kernels are effective in extracting relations that are expressed in multiple sentences. We also show that the graph kernels, namely the ASM and APG kernels, substantially outperform the tree kernels. Among the graph kernels, we showed the ASM kernel as effective for biomedical relation extraction, with comparable performance to the APG kernel for datasets such as the CID-sentence level relation extraction and BioInfer in PPI. Overall, the APG kernel is shown to be significantly more accurate than the ASM kernel, achieving better performance on most datasets.
40 citations
TL;DR: A graph multi-coloring problem where each vertex must be assigned a given number of different colors, represented as integers, and no two adjacent vertices can share a common color is introduced.
27 citations
TL;DR: This paper mainly investigates the Erdős–Gallai-type problems for the monochromatic vertex-connection number mvc(G) and completely determine the exact value, and gives the Nordhaus–Gaddum-type inequality for mVC(G).
Abstract: A path in a vertex-colored graph is called a vertex-monochromatic path if its internal vertices have the same color. A vertex-coloring of a graph is a monochromatic vertex-connection coloring (MVC-coloring for short), if there is a vertex-monochromatic path joining any two vertices in the graph. For a connected graph G, the monochromatic vertex-connection number, denoted by mvc(G), is defined to be the maximum number of colors used in an MVC-coloring of G. These concepts of vertex-version are natural generalizations of the colorful monochromatic connectivity of edge-version, introduced by Caro and Yuster (Discrete Math 311:1786–1792, 2011). In this paper, we mainly investigate the Erdős–Gallai-type problems for the monochromatic vertex-connection number mvc(G) and completely determine the exact value. Moreover, the Nordhaus–Gaddum-type inequality for mvc(G) is also given.
24 citations
TL;DR: In this article, it was shown that for every planar graph on n vertices there is a simultaneous flip of less than 2 n/3 edges to a 4-connected triangulation.
Abstract: We show that every triangulation (maximal planar graph) on n ≥ 6 vertices can be flipped into a Hamiltonian triangulation using a sequence of less than n / 2 combinatorial edge flips. The previously best upper bound uses 4-connectivity as a means to establish Hamiltonicity. But in general about 3 n / 5 flips are necessary to reach a 4-connected triangulation. Our result improves the upper bound on the diameter of the flip graph of combinatorial triangulations on n vertices from 5.2 n − 33.6 to 5 n − 23 . We also show that for every triangulation on n vertices there is a simultaneous flip of less than 2 n / 3 edges to a 4-connected triangulation. The bound on the number of edges is tight, up to an additive constant. As another application we show that every planar graph on n vertices admits an arc diagram with less than n / 2 biarcs, that is, after subdividing less than n / 2 (of potentially 3 n − 6 ) edges the resulting graph admits a 2-page book embedding.
23 citations
TL;DR: An algorithm is described which solves the general problem of determining whether it is possible to delete at most k edges from a given input graph so that the resulting graph avoids a set of forbidden subgraphs, and which is implemented and tested on real datasets based on cattle movements.
Abstract: Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph (of small treewidth) so that the resulting graph avoids a set $$\mathcal {F}$$
of forbidden subgraphs; of particular interest is the problem of determining whether it is possible to delete at most k edges so that the resulting graph has no connected component of more than h vertices, as this bounds the worst-case size of an epidemic. While even this special case of the problem is NP-complete in general (even when $$h=3$$
), we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the general problem in time $$2^{O(|\mathcal {F}|w^r)}n$$
on an input graph having n vertices and whose treewidth is bounded by a fixed constant w, if each of the subgraphs we wish to avoid has at most r vertices. For the special case in which we wish only to ensure that no component has more than h vertices, we improve on this to give an algorithm running in time $$O((wh)^{2w}n)$$
, which we have implemented and tested on real datasets based on cattle movements.
22 citations
TL;DR: It is shown that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean, and a lower bound on the compatibility constant for the total variation penalty is proved.
Abstract: We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs.
As a side result, we get insights into the irrepresentable condition for such tree graphs.
19 citations
06 Sep 2018
TL;DR: In this article, the problem of network design with fees for payment channels from the perspective of a payment service provider (PSP) is studied, and the optimal graph structure and fee assignment to maximize the PSP's profit is examined.
Abstract: Payment channels are the most prominent solution to the blockchain scalability problem We introduce the problem of network design with fees for payment channels from the perspective of a Payment Service Provider (PSP) Given a set of transactions, we examine the optimal graph structure and fee assignment to maximize the PSP’s profit A customer prefers to route transactions through the PSP’s network if the cheapest path from sender to receiver is financially interesting, ie, if the path costs less than the blockchain fee When the graph structure is a tree, and the PSP facilitates all transactions, the problem can be formulated as a linear program For a path graph, we present a polynomial time algorithm to assign optimal fees We also show that the star network, where the center is an additional node acting as an intermediary, is a near-optimal solution to the network design problem
18 citations
TL;DR: In this article, the authors explore the orbit structure and homomesy properties of certain actions of toggle groups on the collection of independent sets of a path graph and prove a generalization of a homomey conjecture of Propp that for the action of a Coxeter element of vertex toggles, the difference of indicator functions of symmetrically-located vertices is 0-mesic.
Abstract: This paper explores the orbit structure and homomesy (constant averages over orbits) properties of certain actions of toggle groups on the collection of independent sets of a path graph. In particular we prove a generalization of a homomesy conjecture of Propp that for the action of a "Coxeter element" of vertex toggles, the difference of indicator functions of symmetrically-located vertices is 0-mesic. Then we use our analysis to show facts about orbit sizes that are easy to conjecture but nontrivial to prove. Besides its intrinsic interest, this particular combinatorial dynamical system is valuable in providing an interesting example of (a) homomesy in a context where large orbit sizes make a cyclic sieving phenomenon unlikely to exist, (b) the use of Coxeter theory to greatly generalize the set of actions for which results hold, and (c) the usefulness of Striker's notion of generalized toggle groups.
18 citations
TL;DR: In this article, a tight sufficient condition for a connected graph with fixed minimum degree to be k-connected based on its spectral radius, for sufficiently large order, is presented, where the spectral radius is defined as the number of vertices in the graph.
Abstract: A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted. In this paper, we present a tight sufficient condition for a connected graph with fixed minimum degree to be k-connected based on its spectral radius, for sufficiently large order.
16 citations
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TL;DR: This work provides an upper bound of the control energy as a function of path length between driver node and target node along an infinite path graph for a single target node and refines the upper bound, by an order of magnitude or more, taking into account not only the length of the path, but also the redundancy of paths.
Abstract: It has recently been shown that the average energy required to control a subset of nodes in a complex network scales exponentially with the cardinality of the subset. While the mean scales exponentially, the variance of the control energy over different subsets of nodes is large and has as of yet not been explained. Here, we provide an explanation of the large variance as a result of both the length of the path that connects control inputs to the target nodes and the redundancy of paths of shortest length. Our first result provides an exact upper bound of the control energy as a function of path length between driver node and target node along an infinite path graph. We also show that the energy estimation is still very accurate even when finite size effects are taken into account. Our second result refines the upper bound that takes into account not only the length of the path, but also the redundancy of paths. We show that it improves the upper bound approximation by an order of magnitude or more. Finally, we lay out the foundations for a more accurate estimation of the control energy for the multi-target and multi-driver problem.
16 citations
TL;DR: In this article, a lower bound on the compatibility constant for the total variation penalty for the Fused Lasso over the path graph was shown. But the compatibility bound was not shown for the case of tree graphs.
Abstract: We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs. As a side result, we get insights into the irrepresentable condition for such tree graphs.
TL;DR: This paper solves the open problem of determining the maximum size of a binary code of constant weight 2 by finding the packing number of the double vertex graph of the path graph that is isomorphic to Sloane’s graph.
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TL;DR: This work introduces the problem of network design with fees for payment channels from the perspective of a Payment Service Provider (PSP), and shows that the star network, where the center is an additional node acting as an intermediary, is a near-optimal solution to the network design problem.
Abstract: Payment channels are the most prominent solution to the blockchain scalability problem. We introduce the problem of network design with fees for payment channels from the perspective of a Payment Service Provider (PSP). Given a set of transactions, we examine the optimal graph structure and fee assignment to maximize the PSP's profit. A customer prefers to route transactions through the PSP's network if the cheapest path from sender to receiver is financially interesting, i.e., if the path costs less than the blockchain fee. When the graph structure is a tree, and the PSP facilitates all transactions, the problem can be formulated as a linear program. For a path graph, we present a polynomial time algorithm to assign optimal fees. We also show that the star network, where the center is an additional node acting as an intermediary, is a near-optimal solution to the network design problem.
TL;DR: It is proved that for a graph G with at least 4 k vertices, if max { d ( x ) , d ( y ) } ≥ 2 k for any pair of nonadjacent vertices , then G contains k disjoint cycles.
TL;DR: Based on new observations and different algorithmic techniques, an O ( n log n ) time algorithm is presented that solves the problem of adding a new edge to P such that the diameter of the resulting graph is minimized.
Abstract: Let P be a path graph of n vertices embedded in a metric space. We consider the problem of adding a new edge to P such that the diameter of the resulting graph is minimized. Previously (in ICALP 2015) the problem was solved in O ( n log 3 n ) time. In this paper, based on new observations and different algorithmic techniques, we present an O ( n log n ) time algorithm.
TL;DR: For n≥3, a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed and has 16 vertices but 44 edges.
Abstract: For n≥3, a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If n≠3, then such a graph has 2n+1 vertices and 2n+2 edges. In the special case when n=3, a smallest graph has 16 vertices but 44 edges.
TL;DR: A system prototype that implements a propose adaptive learning path algorithms that uses the student’s information from their profile and their learning style in order to improve the students’ learning performances through an m-learning system that provides a suitable course content sequence in a personalized manner is proposed.
Abstract: A directed graph represents an accurate picture of course descriptions for online courses through computer-based implementation of various educational systems. E-learning and m-learning systems are modeled as a weighted, directed graph where each node represents a course unit. The Learning Path Graph (LPG) represents and describes the structure of domain knowledge, including the learning goals, and all other available learning paths. In this paper, we propose a system prototype that implements a propose adaptive learning path algorithms that uses the student’s information from their profile and their learning style in order to improve the students’ learning performances through an m-learning system that provides a suitable course content sequence in a personalized manner.
TL;DR: A simple greedy algorithm to totally color a rooted path graph G with at most Δ ( G ) + 2 colors is given, which provides a new proof that the Total Coloring Conjecture holds for rooted path graphs and also proves a useful property of greedy neighborhood coloring for chordal graphs.
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TL;DR: In this paper, an estimate of the minimal solution of a certain algebraic equation is given for the path graph, and an implicit formula for the quadratic embedding constant is derived.
Abstract: A connected graph $G$ is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalently if the quadratic embedding constant $\mathrm{QEC}(G)$ is non-positive For a finite star product of (finite or infinite) graphs $G=G_1\star\dotsb \star G_r$ an estimate of $\mathrm{QEC}(G)$ is obtained after a detailed analysis of the minimal solution of a certain algebraic equation For the path graph $P_n$ an implicit formula for $\mathrm{QEC}(P_n)$ is derived, and by limit argument $\mathrm{QEC}(\mathbb{Z})=\mathrm{QEC}(\mathbb{Z}_+)=-1/2$ is shown During the discussion a new integer sequence is found
TL;DR: In this paper, a family of clique ideals with linear resolutions has been characterized and some homological invariants of the clique ideal of a graph G, which is the complement of a path graph or a cycle graph, are obtained.
Abstract: In this paper, we introduce and study families of squarefree monomial ideals called clique ideals and independence ideals that can be associated to a finite graph. A family of clique ideals with linear resolutions has been characterized. Moreover, some families of graphs for which the quotient ring of their clique ideal is Cohen–Macaulay are introduced and some homological invariants of the clique ideal of a graph G, which is the complement of a path graph or a cycle graph, are obtained. Also some algebraic properties of the independence ideal of path graphs, cycle graphs and chordal graphs are studied.
TL;DR: By employing combinatorial and electrical techniques, it is shown that the conjecture that for a connected n-vertex graph G with a connected complement G ¯ the Kirchhoff index of G, denoted by Kf(G), is the sum of resistance distances between all pairs of vertices in G.
TL;DR: In this article, the authors studied the proper connection number on lexicographic, strong, Cartesian, and direct products of graphs and presented exact values or upper bounds for these products.
Abstract: A path P in an edge-colored graph G is called a proper path if no two adjacent edges of P are colored the same, and G is proper connected if every two vertices of G are connected by a proper path in G. The proper connection number of a connected graph G, denoted by pc(G), is the minimum number of colors that are needed to make G proper connected. In this paper, we study the proper connection number on the lexicographic, strong, Cartesian, and direct products and present exact values or upper bounds for these products of graphs.
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TL;DR: In this paper, a lower bound on the compatibility constant for the total variation penalty for the Fused Lasso over the path graph was shown. But the compatibility bound was not shown for the case of tree graphs with one branch.
Abstract: We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum distance between jumps by the harmonic mean of the distances between jumps. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs. As a side result, we get insights into the irrepresentable condition for the branched path graph.
01 Feb 2018
TL;DR: A new approach for obtaining unique dimensioning for each part and building a full-dimension model of assembly dimensions is presented by describing the formative paths of functional dimensions in an assembly by revising the shortest path graph according to structural characteristics, inspection and dimensioning regulation of parts.
Abstract: This article presents a new approach for obtaining unique dimensioning for each part and building a full-dimension model of assembly dimensions by describing the formative paths of functional dimensions in an assembly. According to the structure and the functional dimensions of an assembly, as well as the principles that ‘the path should be the shortest’, ‘high precision should be given priority’ and ‘one surface can appear only once in the path graph’, the shortest path graph of the functional dimensions can be established first, ensuring that every functional dimension has minimum accumulative errors. The revised path graph is obtained by revising the shortest path graph according to structural characteristics, inspection and dimensioning regulation of parts. In this way, unique dimensioning is achieved for each part, and a full correlative dimension model can be established. A gearbox assembly and a ball screw assembly are used to verify the proposed method, but this article discusses only the assembly...
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TL;DR: New bounds for the number of edges in induced subgraphs of a special distance graph are obtained and these bounds are applied to the graph of LaSalle's inequality.
Abstract: In this article, the author proposes a new approach for the estimating of the number of edges in induced subgraphs of a special distance graph. Author significantly improves previous estimates and suggests a new approach to obtaining better ones.
01 Oct 2018
TL;DR: It is shown that the facility location problem with uniform hard capacities can be solved by the Ageev’s algorithm in \(O(m^3n^2)\) time, where m is the number of facilities and n is thenumber of clients.
Abstract: We show that the facility location problem with uniform hard capacities can be solved by the Ageev’s algorithm in \(O(m^3n^2)\) time, where m is the number of facilities and n is the number of clients. This improves the results \(O(m^5 n^2)\) of Ageev in 2004 and \(O(m^4n^2)\) of Ageev, Gimadi, and Kurochkin in 2009.
TL;DR: In this paper, the dominator chromatic number and domination number are obtained for m-splitting graph and m-shadow graph of path graph and a relationship between them is expressed.
Abstract: Graph theory techniques are applied to several biological domains. The application of graph colouring and domination in the field of biology and medicine includes identifying drug targets, determining the role of proteins, genes of unknown function. The area obtained by combining graph colouring and domination is called the dominator colouring of a graph. This is defined as proper colouring of vertices in which every vertex of the graph dominates all vertices of at least one colour class. The least number of colours required for a dominator colouring of a graph is called the dominator chromatic number. The dominator chromatic number and domination number are obtained for m-Splitting graph and m-Shadow graph of path graph and a relationship between them is expressed in this paper.
TL;DR: The approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user‐friendly ImageJ/Fiji plugin, which relies on the introduction of additional layers in a Viterbi path graph.
Abstract: Motivation:We introduce a formulation for the general task of finding diverse shortest paths between two end-points. Our approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user-friendly ImageJ/Fiji plugin. It relies on the introduction of additional layers in a Viterbi path graph, which requires slight modifications to the standard Viterbi algorithm rules. This layered graph construction allows for the specification of various constraints imposing diversity between solutions. Results:The software allows obtaining a collection of diverse shortest paths under some user-defined constraints through a convenient and user-friendly interface. It can be used alone or be integrated into larger image analysis pipelines. Availability and implementation:http://bigwww.epfl.ch/algorithms/diversepathsj. Contact:michael.unser@epfl.ch or fred.hamprecht@iwr.uni-heidelberg.de. Supplementary information:Supplementary data are available at Bioinformatics online.
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TL;DR: This work constructs some ergodic billiards in 2-balls, where the geodesics bouncing off at the boundary symmetrically and which visit every interior edge exactly once, and tells that every 2-ball can be edge refined using interior edges to become Eulerian if and only if its boundary has length divisible by 3.
Abstract: A finite simple graph is called a 2-graph if all of its unit spheres S(x) are cyclic graphs of length 4 or larger. A 2-graph G is Eulerian if all vertex degrees of G are even. An edge refinement of a graph splits an edge (a,b) to two edges (a,c),(c,b) and connects the newly added vertex c to the intersection of S(a) with S(b). Theorem I assures that every 2-graph can be rendered Eulerian by successive edge refinements. The construction is explicit using geodesic cutting. After the refinement, we have an Eulerian 2-graph that carries a natural geodesic flow. We construct some ergodic ones. A 2-graph with boundary is finite simple graph for which every unit sphere is either a path graph of length n larger than 1 or a cyclic graph of length larger than 3. 2-balls are special 2-graphs are simply connected with a circular boundary. Theorem II tells that every 2-ball can be edge refined using interior edges to become Eulerian if and only if its boundary has length divisible by 3. A billiard map is defined already if all interior vertices have even degree. We will construct some ergodic billiards in 2-balls, where the geodesics bouncing off at the boundary symmetrically and which visit every interior edge exactly once. A consequence of Theorem II is that an Eulerian billiard which is ergodic must have a boundary length that is divisible by 3. We also construct other 2-graphs like tori with ergodic geodesic flows. This clashes with experience in the continuum, where tori have periodic points minimizing the length in homology classes of paths. Ergodic Eulerian 2-graphs or billiards are exciting because they satisfy a Hopf-Rynov result: there exists a geodesic connection between any two vertices. We get so unique canonical metric associated to any ergodic Eulerian graph. It is non-local in the sense that two adjacent vertices can have large distance.
11 Apr 2018
TL;DR: In this paper, a generalization of the MBVST problem is proposed, where the notion of a k-branch vertex is introduced, which is a vertex with degree strictly greater than 2.
Abstract: Given a connected graph \(\mathcal {G}=(\mathcal {V}, \mathcal {E})\) and its spanning tree \(\mathcal {T}\), a vertex \(v \in \mathcal {V}\) is said to be a branch vertex if its degree is strictly greater than 2 in \(\mathcal {T}\). The Minimum Branch Vertices Spanning Tree (MBVST) problem is to find a spanning tree of \(\mathcal {G}\) with the minimum number of branch vertices. This problem has been extensively studied in the literature and has well-developed applications notably related to routing in optical networks. In this paper, we propose a generalization of this problem, where we begin by introducing the notion of a k-branch vertex, which is a vertex with degree strictly greater than \(k+2\). Our goal is to determine a spanning tree of \(\mathcal {G}\) with the minimum number of k-branch vertices (k-MBVST problem). In the context of optical networks, the parameter k can be seen as the limiting capacity of optical splitters to duplicate the input light signal and forward to k destinations. Proofs of NP-hardness and non-inclusion in the APX class of the k-MBVST problem are established for a generic value of k, and then an ILP formulation of the k-MBVST problem based on single commodity flow balance constraints is derived. Computational results based on randomly generated graphs show that the number of k-branch vertices included in the spanning tree increases with the size of the vertex set \(\mathcal {V}\), but decreases with k as well as graph density. We also show that when \(k\ge 4 \), the number of k-branch vertices in the optimal solution is close to zero, regardless of the size and the density of the underlying graph.