Maximum matching

Let ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined as def (G) = max X⊆V (G) (ω0(G -X) -|X|), and this equals the number of vertices unmatched by any maximum matching of Recently a graph operator, called the Dgraph D(G), was defined that has proven very useful in examining Tutte sets and extreme sets of graphs which contain a perfect matching. In this paper we give two natural and related generalizations of the D-graph operator to all simple graphs, both of which have analogues for many of the interesting and useful properties of the original.

A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph G in terms of what is usually called the deficiency. A subset X of V (G) for which this deficiency is attained is called a Tutte set of G. While much is known about maximum matchings, less is known about the structure of Tutte sets. We explored the structural aspects of Tutte sets in another paper. Here, we consider the algorithmic complexity of finding Tutte sets in a graph. We first give two polynomial algorithms for finding a maximal Tutte set. We then consider the complexity of finding a maximum Tutte set, and show it is NP-hard for general graphs, as well as for several interesting restricted classes such as planar graphs. By contrast, we show we can find maximum Tutte sets in polynomial time for graphs of level 0 or 1, elementary graphs, and 1-tough graphs.

Let ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined as def (G) = max X⊆V (G) (ω0(G -X) -|X|), and this equals the number of vertices unmatched by any maximum matching of Recently a graph operator, called the Dgraph D(G), was defined that has proven very useful in examining Tutte sets and extreme sets of graphs which contain a perfect matching. In this paper we give two natural and related generalizations of the D-graph operator to all simple graphs, both of which have analogues for many of the interesting and useful properties of the original.

A well-known formula of Tutte and Berge expresses the size of a maximum matching in a graph G in terms of what is usually called the deficiency. A subset X of V (G) for which this deficiency is attained is called a Tutte set of G. While much is known about maximum matchings, less is known about the structure of Tutte sets. We explored the structural aspects of Tutte sets in another paper. Here, we consider the algorithmic complexity of finding Tutte sets in a graph. We first give two polynomial algorithms for finding a maximal Tutte set. We then consider the complexity of finding a maximum Tutte set, and show it is NP-hard for general graphs, as well as for several interesting restricted classes such as planar graphs. By contrast, we show we can find maximum Tutte sets in polynomial time for graphs of level 0 or 1, elementary graphs, and 1-tough graphs.

This paper studies parallel search algorithms within the framework of independence systems. It is motivated by earlier work on parallel algorithms for concrete problems such as the determination of a maximal independent set of vertices or a maximum matching in a graph and by the general question of determining the parallel complexity of a search problem when an oracle is available to solve the associated decision problem. Our results provide a parallel analog of the self-reducibility process that is so useful in sequential computation.

We show that for every ε > 0 there exist δ > 0 and n0 ∈ N such that every 3-uniform hypergraph on n ≥ n0 vertices with the property that every k-vertex subset, where k ≥ δn, induces at least 1 4 + ε k 3 edges, contains K - 4 as a subgraph, where K - 4 is the 3-uniform hypergraph on 4 vertices with 3 edges. This question was originally raised by Erdős and Sós. The constant 1/4 is the best possible.

We study the minimum spanning tree problem, the maximum matching problem and the shortest path problem subject to binary disjunctive constraints: A negative disjunctive constraint states that a certain pair of edges cannot be contained simultaneously in a feasible solution. It is convenient to represent these negative disjunctive constraints in terms of a so-called conflict graph whose vertices correspond to the edges of the underlying graph, and whose edges encode the constraints. We prove that the minimum spanning tree problem is strongly N Phard, even if every connected component of the conflict graph is a path of length two. On the positive side, this problem is polynomially solvable if every connected component is a single edge (that is, a path of length one). The maximum matching problem is N P-hard for conflict graphs where every connected component is a single edge. Furthermore we will also investigate these graph problems under positive disjunctive constraints: In this setting for certain pairs of edges, a feasible solution must contain at least one edge from every pair. We establish a number of complexity results for these variants including APX-hardness for the shortest path problem.

The main objective of our work is to align multiple sequences together on the basis of statistical approach in lieu of heuristics approach. Here we are proposing a novel idea for aligning multiple sequences in which we will be considering the DNA sequences as lines not as strings where each character represents a point in the line. DNA sequences are aligned in such a way that maximum overlap can occur between them, so that we get maximum matching of characters which will be treated as our seeds of the alignment. The proposed algorithm will first find the seeds in the aligning sequences and then it will grow the alignment on the basis of statistical approach of curve fitting using standard deviation.

We consider a relaxation of the concept of well-covered graphs, which are graphs with all maximal independent sets of the same size. The extent to which a graph fails to be well-covered can be measured by its independence gap, defined as the difference between the maximum and minimum sizes of a maximal independent set in G. While the wellcovered graphs are exactly the graphs of independence gap zero, we investigate in this paper graphs of independence gap one, which we also call almost well-covered graphs. Previous works due to Finbow et al. and Barbosa et al. have implications for the structure of almost well-covered graphs of girth at least k for k ∈ {7, 8}. We focus on almost well-covered graphs of girth at least 6. We show that every graph in this class has at most two vertices each of which is adjacent to exactly 2 leaves. We give efficiently testable characterizations of almost well-covered graphs of girth at least 6 having exactly one or exactly two such vertices. Building on these results, we develop a polynomial-time recognition algorithm of almost well-covered {C3, C4, C5, C7}-free graphs.

We consider a relaxation of the concept of well-covered graphs, which are graphs with all maximal independent sets of the same size. The extent to which a graph fails to be well-covered can be measured by its independence gap, defined as the difference between the maximum and minimum sizes of a maximal independent set in G. While the wellcovered graphs are exactly the graphs of independence gap zero, we investigate in this paper graphs of independence gap one, which we also call almost well-covered graphs. Previous works due to Finbow et al. and Barbosa et al. have implications for the structure of almost well-covered graphs of girth at least k for k ∈ {7, 8}. We focus on almost well-covered graphs of girth at least 6. We show that every graph in this class has at most two vertices each of which is adjacent to exactly 2 leaves. We give efficiently testable characterizations of almost well-covered graphs of girth at least 6 having exactly one or exactly two such vertices. Building on these results, we develop a polynomial-time recognition algorithm of almost well-covered {C3, C4, C5, C7}-free graphs.

We consider a relaxation of the concept of well-covered graphs, which are graphs with all maximal independent sets of the same size. The extent to which a graph fails to be well-covered can be measured by its independence gap, defined as the difference between the maximum and minimum sizes of a maximal independent set in G. While the well-covered graphs are exactly the graphs of independence gap zero, we investigate in this paper graphs of independence gap one, which we also call almost well-covered graphs. Previous works due to Finbow et al. (1994) and Barbosa et al. (2013) have implications for the structure of almost well-covered graphs of girth at least k for k∈{7,8}. We focus on almost well-covered graphs of girth at least 6. We show that every graph in this class has at most two vertices each of which is adjacent to exactly 2 leaves. We give efficiently testable characterizations of almost well-covered graphs of girth at least 6 having exactly one or exactly two such vertices....

We study graphs in which the maximum and the minimum sizes of a maximal independent set differ by exactly one. We call these graphs almost well-covered, in analogy with the class of well-covered graphs, in which all maximal independent sets have the same size. A characterization of graphs of girth at least $8$ having exactly two different sizes of maximal independent sets due to Finbow, Hartnell, and Whitehead implies a polynomial-time recognition algorithm for the class of almost well-covered graphs of girth at least $8$. We focus on the structure of almost well-covered graphs of girth at least $6$. We give a complete structural characterization of a subclass of the class of almost well-covered graphs of girth at least $6$, a polynomially testable characterization of another one, and a polynomial-time recognition algorithm of almost well-covered $\{C_3,C_4,C_5,C_7\}$-free graphs.

The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n 2 and α ′ = a, or (2) a < n 2 and there is a vertex , where α ′ is the critical independence number of the graph. Furthermore, we show that it can be determined in polynomial time whether α = a. Finally we show that a graph where α = a is either König-Egerváry or almost König-Egerváry. the electronic journal of combinatorics 18 (2011), #P180 2 and it follows that J c contains a vertex u. Suppose N(J c ) = ∅. So J c is an isolated set of vertices and α ′ (G -J c ) = 0 and It again follows that J c is a maximum independent set and G is an empty graph. It was noted earlier that the theorem follows for these graphs. So it can be assumed that N(J c ) = ∅. Let w be a vertex in N(J c ). It follows from Theorem 2.1 that J c is contained in a maximum independent set I. Since w / ∈ I, w is not in every maximum independent set of G. Thus, Equation (1) holds. It is enough to show then that α ′ (G) = α ′ (Gw). Let N H (Y ) be the neighbors of a set Y of vertices in a graph H. There are two cases to consider: (1) the case where w ∈ N G (J ′ c ), and (2) the case where , proving in this case too that α ′ (G) = α ′ (Gw). Let G be a graph. The steps to determine whether α(G) = a(G) are as follows. the electronic journal of combinatorics 18 (2011), #P180

In this paper we study relationships between the matching number, written µ(G), and the independence number, written α(G). Our first main result is to show where X is any intersection of maximum independent sets in G. Our second main result is to show where δ(G) and ∆(G) denote the minimum and maximum vertex degrees of G, respectively. These results improve on and generalize known relations between µ(G) and α(G). Further, we also give examples showing these improvements.

The annihilation number $a$ of a graph is an upper bound of the independence number $\alpha$ of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that $\alpha=a$ if, and only if, either (1) $a\geq \frac{n}{2}$ and $\alpha&#39; =a$, or (2) $a &lt; \frac{n}{2}$ and there is a vertex $v\in V(G)$ such that $\alpha&#39; (G-v)=a(G)$, where $\alpha&#39;$ is the critical independence number of the graph. Furthermore, we show that it can be determined in polynomial time whether $\alpha=a$. Finally we show that a graph where $\alpha=a$ is either König-Egerváry or almost König-Egerváry.

For a fixed family F of graphs, an F -packing in a graph G is a set of pairwise vertexdisjoint subgraphs of G, each isomorphic to an element of F . Finding an F -packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K 2 }. In this paper we provide new approximation algorithms and hardness results for the K r -packing problem where K r = {K 2 , K 3 , . . . , K r }. We show that already for r = 3 the K r -packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2approximation, achieving a known ratio that follows from a more involved algorithm of Halldórsson. For r = 4, we obtain a (3/2 + )-approximation, and for r = 5 we obtain a (25/14 + )-approximation.

The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as König-Egerváry graphs. König-Egerváry graphs have been studied extensively from a graph theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding maximum König-Egerváry subgraphs of a given graph. More specifically, we look at the problem of finding a minimum number of vertices or edges to delete to make the resulting graph König-Egerváry. We show that both these versions are NP-complete and study their complexity from the points of view of approximation and parameterized complexity. En route, we point out an interesting connection between the vertex deletion version and the A G V C problem where one is interested in the parameterized complexity of the V C problem when parameterized by the 'additional number of vertices' needed beyond the matching size. This connection is of independent interest and could be useful in establishing the parameterized complexity of A G V C problem.

In every high frequency transport system, the problem of regularity is critical. Randomness can increase passenger's travel time. We focus the attention on the real-time deadheading problem, because deadheading is the only way that allows to re-establish the correct headway without increase of the lap time. When a vehicle is deadheaded, it runs empty from a terminal skipping a number of stations, typically in order to reduce expected large headways at later stations. The objective is to determine the optimal number of stations to skip in order to minimize passenger's total travel time.

Microarray gene cxprl!.~sion arrays are widely uscd in biological rcscnrches. WII!!n lhe genes are followed ai severa! lime painl", Ihose arrays would givc a time-series for each gene. Usual c1ustering rncthods. sueh as k-means or hierarchical clustering mcthods cannat bc applicd on time-scries. sincc Ibey do nol consider lhe dcpendcncc bctwecn lhe values at dirrcrcnt time points for a spccific gene. \Ve propose a melhod which lakes Ihis dependence into consider, and moreover, finds lhe interesting genes which show different pallems in differenl samples or condilions (e.g. contrai and trcalmenl).

The stability number of a graph G, denoted by α(G), is the cardinality of a maximum stable set, and µ(G) is the cardinality of a maximum matching in G. If α(G) + µ(G) equals its order, then G is a König-Egerváry graph. In this paper we deal with square-stable graphs, i.e., the graphs G enjoying the equality α(G) = α(G 2 ), where G 2 denotes the second power of G. In particular, we show that a König-Egerváry graph is square-stable if and only if it has a perfect matching consisting of pendant edges, and in consequence, we deduce that well-covered trees are exactly the square-stable trees.

A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph spanned by S ∪ N (S), where N (S) is the neighborhood of S. A matching M is uniquely restricted if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself. Nemhauser and Trotter Jr. , proved that any S ∈ Ψ(G) is a subset of a maximum stable set of G. In we have shown that the family Ψ(T ) of a forest T forms a greedoid on its vertex set. In this paper we demonstrate that for a bipartite graph G, Ψ(G) is a greedoid on its vertex set if and only if all its maximum matchings are uniquely restricted.

The stability number of the graph G, denoted by α(G), is the cardinality of a maximum stable set of G. A graph is well-covered if every maximal stable set has the same size. G is a König-Egerváry graph if its order equals α(G) + µ(G), where µ(G) is the cardinality of a maximum matching in G. In this paper we characterize α ++ -stable graphs, namely, the graphs whose stability numbers are invariant to adding any two edges from their complements. We show that a König-Egerváry graph is α ++ -stable if and only if it has a perfect matching consisting of pendant edges and no four vertices of the graph span a cycle. As a corollary it gives necessary and sufficient conditions for α ++ -stability of bipartite graphs and trees. For instance, we prove that a bipartite graph is α ++ -stable if and only if it is well-covered and C4-free.

Let $G$ be a simple graph with vertex set $V\left( G\right) $. A set $S\subseteq V\left( G\right) $ is independent if no two vertices from $S$ are adjacent, and by $\mathrm{Ind}(G)$ we mean the family of all independent sets of $G$. The number $d\left( X\right) =$ $\left\vert X\right\vert -\left\vert N(X)\right\vert $ is the difference of $X\subseteq V\left( G\right) $, and a set $A\in\mathrm{Ind}(G)$ is critical if $d(A)=\max \{d\left( I\right) :I\in\mathrm{Ind}(G)\}$ (Zhang, 1990). Let us recall the following definitions: $\mathrm{core}\left( G\right) $ = $\bigcap$ {S : S is a maximum independent set}. $\mathrm{corona}\left( G\right)$ = $\bigcup$ {S :S is a maximum independent set}. $\mathrm{\ker}(G)$ = $\bigcap$ {S : S is a critical independent set}. $\mathrm{diadem}(G)$ = $\bigcup$ {S : S is a critical independent set}. In this paper we present various structural properties of $\mathrm{\ker}(G)$, in relation with $\mathrm{core}\left( G\right) $, $\mathrm{corona}\left( G\right) $...

An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while µ(G) is the cardinality of a maximum matching. If s k is the number of independent sets of size k in G, then and Harary, 1986). If s j = s α-j for all 0 ≤ j ≤ α/2 , then I(G; x) is called symmetric (or palindromic). It is known that the graph G • 2K 1 , obtained by joining each vertex of G to two new vertices, has a symmetric independence polynomial . In this paper we develop a new algebraic technique in order to take care of symmetric independence polynomials. On the one hand, it provides us with alternative proofs for some previously known results. On the other hand, this technique allows to show that for every graph G and for each non-negative integer k ≤ µ (G), one can build a graph H, such that: G is a subgraph of H, I (H; x) is symmetric, and I (G • 2K 1 ; x) = (1 + x) k • I (H; x).

A set S of vertices is independent in a graph G, and we write S ∈ Ind(G), if no two vertices from S are adjacent, and α(G) is the cardinality of an independent set of maximum size, while core(G) denotes the intersection of all maximum independent sets . G is called a König-Egerváry graph if its order equals α(G) + µ(G), where µ(G) denotes the size of a maximum matching. The number def , where N (S) is the neighborhood of S, and αc(G) denotes the maximum size of a critical independent set . In it was shown that G is König-Egerváry graph if and only if there exists a maximum independent set that is also critical, i.e., αc(G) = α(G). In this paper we prove that: (ii) G is König-Egerváry graph if and only if each maximum independent set of G is critical.

A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈ (G), if S is a maximum stable set of the subgraph spanned by S ∪ N (S), where N (S) is the neighborhood of S. A matching M is uniquely restricted if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself. Nemhauser and Trotter Jr. (Math. Programming 8(1975) 232-248), proved that any S ∈ (G) is a subset of a maximum stable set of G. In Levit and Mandrescu (Discrete Appl. Math., 124 (2002) 91-101) we have shown that the family (T ) of a forest T forms a greedoid on its vertex set. In this paper, we demonstrate that for a bipartite graph G, (G) is a greedoid on its vertex set if and only if all its maximum matchings are uniquely restricted.

A matching M is uniquely restricted in a graph G if its saturated vertices induce a subgraph which has a unique perfect matching, namely M itself [M.C. Golumbic, T. Hirst, M. Lewenstein, Uniquely restricted matchings, Algorithmica 31 (2001) 139-154]. G is a König-Egerváry graph provided (G) + (G) = |V (G)| [R.W. Deming, Independence numbers of graphs-an extension of the König-Egerváry theorem, Discrete Math. 27 (1979) 23-33; F. Sterboul, A characterization of the graphs in which the transversal number equals the matching number, J. Combin. Theory Ser. B 27 (1979) 228-229], where (G) is the size of a maximum matching and (G) is the cardinality of a maximum stable set. S is a local maximum stable set of G, and we write S ∈ (G), if S is a maximum stable set of the subgraph spanned by S ∪ N(S), where N(S) is the neighborhood of S. Nemhauser and Trotter [Vertex packings: structural properties and algorithms, Math. Programming 8 (1975) 232-248], proved that any S ∈ (G) is a subset of a maximum stable set of G. In [V.E. Levit, E. Mandrescu, Local maximum stable sets in bipartite graphs with uniquely restricted maximum matchings, Discrete Appl. Math. 132 (2003) 163-174] we have proved that for a bipartite graph G, (G) is a greedoid on its vertex set if and only if all its maximum matchings are uniquely restricted. In this paper we demonstrate that if G is a triangle-free graph, then (G) is a greedoid if and only if all its maximum matchings are uniquely restricted and for any S ∈ (G), the subgraph spanned by S ∪ N(S) is a König-Egerváry graph.

Abstract. The stability number of the graph G, denoted by α (G), is the cardinality of a maximum stable set of G. In this paper we characterize the square-stable graphs, ie, the graphs enjoying the property α (G)= α (G 2), where G 2 is the graph with the same vertex set as in G, and an edge of G 2 is joining two distinct vertices, whenever the distance between them in G is at most 2. We show that every square-stable graph is well-covered, and wellcovered trees are exactly the square-stable trees. Keywords: stable set, square-stable ...

G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S∈ Ψ (G), if S is a maximum stable set of the subgraph induced by S∪ N (S), where N (S) is the neighborhood of S.

Optical communication is a promising candidate for many emerging networking and parallel/distributed computing applications because of its huge bandwidth. Wavelength Division Multiplexing (WDM) is a technique that can better utilize the optical bandwidth by dividing the bandwidth of a fiber into multiple wavelength channels. In this paper, we study optimal scheduling algorithms to resolve output contentions in bufferless time slotted WDM optical interconnects with wavelength conversion ability. We consider the general case of limited range wavelength conversion with arbitrary conversion capability, as limited range wavelength conversion is easier to implement and more cost effective than full range wavelength conversion, and it also includes full range wavelength conversion as a special case. We first consider the conversion scheme in which each wavelength can be converted to multiple wavelengths in an interval of wavelengths and the intervals for different wavelengths are "ordered." We show that the problem of maximizing network throughput can be formalized as finding a maximum matching in a bipartite graph. We then give an optimal scheduling algorithm called the First Available Algorithm that runs in OðkÞ time, where k is the number of wavelengths per fiber. We also study the case where the connection requests have different priorities. We formalize the problem as finding an optimal matching in a weighted bipartite graph and give a scheduling algorithm called the Downwards Expanding Algorithm that runs in OðkD þ Nk logðNkÞÞ time where N is the number of input fibers of the interconnect and D is the conversion degree. Finally, we consider the circular symmetrical wavelength conversion scheme and give optimal scheduling algorithms for nonprioritized scheduling in OðDkÞ time and prioritized scheduling in Oðk 2 þ Nk logðNkÞÞ time.

In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: ... 1. Initialization Time: O(n(log(n))) to build the Top-tree.

Word segmentation is one of the most important tasks in NLP. This task, within Vietnamese language and its own features, faces some challenges, especially in words boundary determination. To tackle the task of Vietnamese word segmentation, in this paper, we propose the WS4VN system that uses a new approach based on Maximum matching algorithm combining with stochastic models using part-of-speech information. The approach can resolve word ambiguity and choose the best segmentation for each input sentence. Our system gives a promising result with an F-measure of 97%, higher than the results of existing publicly available Vietnamese word segmentation systems.

dégradation des performances d'un tag particulier dans une configuration donnée de tags environnants est évaluée individuellement, les moments statistiques ainsi que les fonctions de répartition permettent de prédire le comportement d'une population de tags sous certaines conditions. Cette thèse aide le concepteur RFID à évaluer la performance d'un scénario RFID et éventuellement à ajuster certains paramètres d'entrée tels que la densité des tags afin d'atteindre les objectifs visés.

Abstract: The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact graphs and surfaces. It is an extension to the non-compact case of the concept of critical simplex which takes into account the monotonous ...

In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: ... 1. Initialization Time: O(n(log(n))) to build the Top-tree.

More and more people rely on Web information and with the advance of Web 2.0 technologies they can increasingly easily participate to the creation of this information. Country-level politicians could not ignore this trend and have started to use the Web to promote them or to demote their opponents. This paper presents how candidates to a French mayor local election and with less budget have engineered their Web campaign and online reputation. After presenting the settings of the local election, the Web tools used by the different candidates and the local journalists are detailed. These tools are evaluated from a security point of view and the legal issues that they have created are underlined.

The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies for acceptance, a thesis entitled "Dynamic and Self-stabilizing Distributed Matching" submitted by Subhendu Chattopadhyay in partial fulfillment of the requirements for the degree of Master of Science.

It is generafly believed that words, rather than characters, should be the smallest indexing unit for Chinese text retrieval systems, and that it is essential to have a comprehensive Chinese dictionary or lexicon for Chhmse text retrieval systems to do well. Chinese text has no delimiters to mark woni boundaries. As a result, any text retrieval systems that build word-based indexes need to segment text into words. We implemented several statistical and dictionary-hazed word segmentation methods to study the effect on retrieval effectiveness of different segmentation methods using the TREC-S Chinese test collection and topics. The results show that, for all three sets of queries, the simple bigram indexing and the purely statistical word segmentation perform better than the popular dictionary-based maximum matching method with a dictionary of 138,955 entries.

It is generafly believed that words, rather than characters, should be the smallest indexing unit for Chinese text retrieval systems, and that it is essential to have a comprehensive Chinese dictionary or lexicon for Chhmse text retrieval systems to do well. Chinese text has no delimiters to mark woni boundaries. As a result, any text retrieval systems that build word-based indexes need to segment text into words. We implemented several statistical and dictionary-hazed word segmentation methods to study the effect on retrieval effectiveness of different segmentation methods using the TREC-S Chinese test collection and topics. The results show that, for all three sets of queries, the simple bigram indexing and the purely statistical word segmentation perform better than the popular dictionary-based maximum matching method with a dictionary of 138,955 entries.

Ubiquitous data flow through a directed complex network requires the complete structural controllability of the network. For evaluating the structural controllability of any network, determination of maximum matching in the network is a cardinal task and has always been a problem of immense concern. Its solution is mandatory in structural control theory for controlling real world complex networks. The existing classical approach through the Hopcroft-Karp algorithm and other proposed algorithms require the determination of the bipartite equivalent graph (i.e., network), which belongs to the NP-complete class of problems. In this article, we propose a degree-first greedy search algorithm to determine maximum matching in unipartite graphs without determining its bipartite equivalent. Thus this classical problem of the NP-Complete class can be solved using the heuristic, with

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every non-maximum matching has an augmenting path of length O(log n). This implies that augmenting path algorithms like the Hopcroft-Karp algorithm for bipartite graphs and the Micali-Vazirani algorithm for general graphs, which have a worst case running time of O(m √ n), run in time O(m log n) with high probability, where m is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least ln(n) [Average Case Analysis of Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6):1329-1356, 1994]. Our results hold if only the average degree is a large enough constant. At the same time we simplify the analysis of Motwani.

Word segmentation is one of the most important tasks in NLP. This task, within Vietnamese language and its own features, faces some challenges, especially in words boundary determination. To tackle the task of Vietnamese word segmentation, in this paper, we propose the WS4VN system that uses a new approach based on Maximum matching algorithm combining with stochastic models using part-of-speech information. The approach can resolve word ambiguity and choose the best segmentation for each input sentence. Our system gives a promising result with an F-measure of 97%, higher than the results of existing publicly available Vietnamese word segmentation systems.

Using virtual output queueing(VOQ), maximum matching scheduling slgorithms have been shown to achieve 100% throughput in input-queued switches, but has high complexity such that implementation is infensible for high-speed systems Iterative maximal matching algorithms, proposed as an allemative, cannnt run L r more than B few iterations due to the hardware complexity involved, fhus resulthg in low throughput. In this paper, we intruduce a starvation-free iterative maximal matching algorithm called Highest Count First (iHCF). The iHCF algorithm gives preferential service based on l h c approximate age of the head-of-line cell in a VOQ and maximizes the size of the matching using round-robin priority pointers. We show that iHCF can a&ieve 100% throughput under Ll.d and uniform t M c in a single iteration. We also show using simulations that it performs as well as other known practical algorithms and achieves 100% throughput when run for only a few iterations under dif'ferent admissible traflic patterns Compared to other algorithms, iHCF lends lo a low complexity architecture such that the scheduling does not become the bottleneck.

A clutter (or antichain or Sperner family) L is a pair (V, E), where V is a finite set and E is a family of subsets of V none of which is a subset of another. Usually, the elements of V are called vertices of L, and the elements of E are called edges of L. A subset s e of an edge e of a clutter is called recognizing for e, if s e is not a subset of another edge. The hardness of an edge e of a clutter is the ratio of the size of e's smallest recognizing subset to the size of e. The hardness of a clutter is the maximum hardness of its edges. We study the hardness of clutters arising from independent sets and matchings of graphs.

Let f (n, r, k) be the minimal number such that every hypergraph larger than f (n, r, k) contained in [n] r contains a matching of size k, and let g(n, r, k) be the minimal number such that every hypergraph larger than g(n, r, k) contained in the r-partite r-graph [n] r contains a matching of size k. The Erdős-Ko-Rado theorem states that f (n, r, 2) = n−1 r−1 (r ≤ n 2) and it is easy to show that g(n, r, k) = (k − 1)n r−1. The conjecture inspiring this paper is that if F 1 , F 2 ,. .. , F k ⊆ [n] r are of size larger than f (n, r, k) or F 1 , F 2 ,. .. , F k ⊆ [n] r are of size larger than g(n, r, k) then there exists a rainbow matching, i.e. a choice of disjoint edges f i ∈ F i. In this paper we deal mainly with the second part of the conjecture, and prove it for r ≤ 3. We also prove that for every r and k there exists n 0 = n 0 (r, k) such that the r-partite version of the conjecture is true for n > n 0 .

We develop an algorithmic framework to decompose a collection of time-stamped text documents into semantically coherent threads. Our formulation leads to a graph decomposition problem on directed acyclic graphs, for which we obtain three algorithms-an exact algorithm that is based on minimum cost flow and two more efficient algorithms based on maximum matching and dynamic programming that solve specific versions of the graph decomposition problem. Applications of our algorithms include superior summarization of news search results, improved browsing paradigms for large collections of text-intensive corpora, and integration of time-stamped documents from a variety of sources. Experimental results based on over 250,000 news articles from a major newspaper over a period of four years demonstrate that our algorithms efficiently identify robust threads of varying lengths and time-spans.