Algorithms on graphs, excluding heuristics.

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Which graph problems are $W[1]$-Hard on directed(/weighted) graphs but FPT on undirected(/unweighted) graphs?

Following the equivalent questions regarding NP-Completeness (see the weight question and the directed question), I was wondering how parameterized problems are affected by these attributes. ...
0
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28 views

DAG reduce edges by transitivity

I have a DAG like this $G_1 = \lbrace A \to B \to C \rbrace$ My algorithm modify $G_1$ so it will be like this $ G_2 = \lbrace A \to C, B \to C \rbrace $ I now that $G_2$ is not a transitive ...
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24 views

Big O notation for vectors - basic algorithm [on hold]

I would like to insert data from one vector to another if its element satisfies some conditions My algorithm is like this ...
2
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0answers
119 views

How much faster is solving Clique in properly colored graph?

Given a graph $G$ and a proper vertex coloring $C$ with the minimum numbers of colors, how much faster can a maximum clique be found than when just $G$ is given? Additional information doesn't make ...
0
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1answer
33 views

polytime transformation from a graph to a set of binary strings

$d_H$ denotes the Hamming distance between two binary strings of the same size. The problem is stated as follows. Given any undirected graph $(V, A)$, does there always exist a one-to-one ...
3
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3answers
190 views

Minimum vertex cover on k-regular graphs, for fixed k>2 NP-hard proof?

Good Evening! I am aware that the minimum (cardinality) vertex cover problem on cubic graphs ($3$-regular) graphs is $NP$-hard. Say positive integer $k>2$ is fixed. Has there been any ...
3
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1answer
177 views

Graph with minimum number of edges having given sets of nodes as its paths

Consider the following problem: Input: a list of subsets $P_1, P_2, \ldots, P_k \subseteq V = \{1, \ldots, n\}$ Output: a graph $G = (V,E)$ with minimum number of edges such that for every $P_i$ ...
-3
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1answer
51 views

Leader election algorithm in a grid

I have to write a leader election algorithm in an unoriented mesh (a grid a*b), with many initiators. Someone give me an indication to wake up each node and then make an election in the exterior ring ...
3
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0answers
113 views

Equivalence of deterministic finite transducers over finite/infinite words

Equivalence of deterministic finite transducers - a special case of single-valued finite transducers - is decidable because it is decidable whether a transducer is single-valued. Note that two ...
2
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56 views

What mathematical models can analyze and optimize such message passing system?

I look for a mathematical model that can accommodate, analyze and suggest optimizations for a system that can be humanly described as message passing black box programs to which where optimal message ...
0
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0answers
34 views

Graph generation model effect on performance of Spectral graph algorithms

I use spectral graph algorithms for finding community structures, specifically the Leading Eigenvector Method (http://arxiv.org/abs/physics/0605087). I try analyzing the performance of these ...
15
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1answer
344 views

Is this dense version of Kruskal's algorithm well-known?

About a year ago, a friend and I thought of a way to implement Kruskal's algorithm for dense graphs in better than the usual $O(m \log m)$ bound (without assuming pre-sorted edges). Specifically, we ...
3
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0answers
49 views

Existing technique to detect the clique and biclique cover the edges in a graph?

I wonder if there is any existing method to find the clique and biclique structures in a graph that can cover all the edges in it, and every edge belongs to exactly one of the cliques or bicliques ...
5
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1answer
112 views

Why does the transformation in the proof for SL=L preserve connectedness of s and t?

I'm currently working on this paper showing that $\mathcal{SL} = \mathcal{L}$. But I keep wondering how the transformation $\tau$ in definition 3.1 preserves the connectivity of $s$ and $t$. $\tau$ ...
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0answers
49 views

Realization of a bipolar orientation by a mixed graph

Given an undirected graph $G(V,E)$ and a bipolar orientation $s$ over $G$, consider the problem of identifying $s$ by finding the minimum number of edges such that when orienting them in a particular ...
0
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0answers
44 views

Total number of spanning trees of a set of graphs with constraint

This is an extension of the question "Total number of spanning trees of a set of graphs". The original problem has been shown to be #P-complete. Now a new constraint is added to the problem. I have ...
6
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0answers
99 views

Maximum weight “fair” matching

I'm interested in a variant of the maximum weight matching in a graph, which I call "Maximum Fair Matching". Assume that the graph is full (i.e. $E=V\times V$), has even number of vertices, and that ...
0
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0answers
52 views

Extending clique-percolation to bipartite graphs

Clique percolation is well-defined for general graphs. In bigraphs, however, there are only 2-cliques, so the algorithm does not work. There a several extensions of the definition of a clique for ...
0
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1answer
114 views

checking isomorphism between K regular graph

Problem Input is a k regular graph of n vertices and I have to check whether this is isomorphic to another given k regular graph G. This is a restricted version of graph isomorphism in the sense that ...
2
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1answer
97 views

State of the art algorithms for community detection in graphs

Is anyone aware of the must read papers to get knowledge of the most recent algorithms and method for community detection in graphs, especially those that represent social networks?
0
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0answers
38 views

Number of k-expressions of graph (clique Width)

The clique-width of a graph $G$ is the minimum number of labels needed to construct G by means of the following 4 operations. The Construction of a graph $G$ using the four operations is represented ...
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2answers
114 views

Finding the paths through a graph that reuse as many of the nodes as possible

I'm implementing an encryption algorithm which does a bunch xor operations to mix up the columns. Because I want to find the lower bound of the number of ...
2
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2answers
97 views

Graphs whose maximal clique intersection graph has bounded chromatic number

In general, The chromatic number of the clique intersection graph a graph can again be arbitrarily high. For example, take $n$ maximal cliques of size $n$ such that every pair of maximal cliques has ...
2
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1answer
183 views

Modifying Hopcroft-Karp algorithm to get approximate bipartite matching

I am trying to find an algorithm to find an $\epsilon$-approximate maximum matching $M_{\epsilon}$ in a bipartite graph in $O(m/\epsilon)$. The partite groups are of equal size, they are $A$ and $B$. ...
4
votes
1answer
154 views

Total number of spanning trees of a set of graphs

Given an undirected graph G with $n$ nodes, we can compute its number of spanning trees in polynomial time using Kirchhoff's matrix-tree theorem. Now consider a more complicated setting, in which each ...
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2answers
137 views

Upper bound for number of independent sets

What is the tightest upper bound known for the number of independent sets in a graph?
5
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80 views

The distribution on the solution space induced by randomized rounding

Consider the Goemans-Williamson algorithm for the MAX-CUT problem. It is known, that if $maxcut(G) \geq 1-\epsilon$, then the algorithm returns a cut $S$ of fractional size at least ...
5
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1answer
88 views

Expected length of longest construction path in Barabási–Albert Model

The Barabási-Albert Model is used for constructing scale-free networks using the preferential attachment technique. The essence, as I understand it, is that nodes are incrementally added to a graph by ...
0
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4answers
252 views

Finding outer face in plane graph (embedded planar graph)

I have a planar graph, for which I have computed a combinatorial embedding and coordinates in the plane. So all my arcs are now oriented in the plane, respective to their end vertices. Computing a ...
7
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2answers
209 views

Enumerating Planar Graphs of Bounded Treewidth

I am looking for references for the following problem: given integers $n$ and $k$, enumerate all non-isomorphic planar graphs on $n$ vertices and treewidth $\leq k$. I'm interested both in theoretical ...
3
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0answers
73 views

Definition of Clique width of graph

The clique width of graph $G$ is defined as minimum number of labels required to construct $G$ by using four operations. I would like to know why the name clique width is given to this definition. ...
4
votes
1answer
84 views

How to Quantify Entropy in a Data Set

I'm currently creating a program in Java to analysis the pathological cases of Quicksort. Namely, the transition of complexity from O(n^2) to O(nlogn) as a data set gets less ordered. Since Quicksort ...
6
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0answers
78 views

Fully dynamic algorithms for strong components of a directed graph

I'm faced with the problem of maintaining the strong components of a directed graph under insertions/deletions of edges and vertices. As noted in one of the answers to a closely-related question ...
3
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1answer
76 views

Graph (Forest) representation that supports edge deletion and efficient traversal

I am trying to write a data structure that given a general tree (or forest) will support the following operations: Edge deletion Connected(u,v) queries This problem is addressed in section two of ...
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1answer
98 views

Connecting partial paths to form a hamiltonian cycle [closed]

For an undirected graph that consists of partial paths such that each vertex is a part of one of those paths and that there are edges between all the paths, is there an efficient algorithm to connect ...
8
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1answer
153 views

Efficient Reduction from Min Cut to st-Min Cut

I am aware that many known algorithms for min cut problem is not by reducing the problem to $st$-min cut. But the question of efficient reduction from min cut to $st$-min cut is still interesting to ...
7
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2answers
469 views

How can I find the second cheapest spanning tree?

The classic Mininum Spanning Tree (MST) algorithms can be modified to find the Maximum Spanning Tree instead. Can an algorithm such as Kruskal's be modified to return a spanning tree that is strictly ...
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1answer
137 views

Finding cliques in weighted graph

We have given a weighted graph $G=\{V,E\}$, where $V=\{v_1, v_2,...,v_n\}$, and for all $i,j$, the weight of edges $w(v_i, v_j)\in (0,W)$. And we have also given a weight threshold s $w$ (where ...
4
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2answers
217 views

Find the cheapest cycle through two points on a rectangular grid

I have a task, but I have no idea how to solve it. We have to find a cycle going through $(1,1)$ and $(n,n)$ (X axis on the picture is indexed right to left) such that the sum of values in cells is ...
6
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2answers
343 views

Complexity of finding even cuts for a graph

Given a graph $G=(V,E)$, what is known about the classical computational complexity of finding a non-trivial cut which partitions the vertices into two sets $V_a$ and $V_b$ such that every vertex in ...
6
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0answers
87 views

General Results for Complicated Constraint Satisfaction Problem

Consider the following problem: on a finite two-dimensional grid (say the grid points are vertices of a graph), I need to color the vertices in such a way to satisfy the existence and nonexistence of ...
3
votes
2answers
104 views

Hamiltonian cycle on a subset of 2D points, constrained by maximum total length

We are given a list of 2d coordinates, each coordinate representing a node in a graph, and a scalar D, which is a constraint on total length of the cycle. The task is to find a Hamiltonian cycle on a ...
11
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0answers
118 views

Lower bounds on single-source shortest paths in directed graphs

Are there any non-trivial lower bounds on the complexity of single-source shortest paths (SSSP) in a directed graph, where all edges have non-negative edge weights? Can we rule out the possibility of ...
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1answer
91 views

Minimum vertex cover for bipartite graphs

I know that it is possible to calculate the minimum vertex cover of a bipartite graph, However, i want that the minimum vertex cover which contains vertices from only one partite set, which will be ...
15
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3answers
321 views

What separates easy global problems from hard global problems on graphs of bounded treewidth?

Plenty of hard graph problems are solvable in polynomial time on graphs of bounded treewidth. Indeed, textbooks typically use e.g. independet set as an example, which is a local problem. Roughly, a ...
2
votes
1answer
159 views

Max flow: either saturate an edge or avoids

Is there a way to create a max flow graph such that it satisfies the condition that a flow either saturates an edge or completely avoids it. It can't have half its flow through one edge and half ...
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1answer
97 views

Finding an exactly weighted st-path in a digraph [closed]

I have a weighted digraph graph $G = (V,E)$ where the weights are positive and negative integers. The graph $G$ is not necessarily acyclic. The question is: given 2 nodes $v_1$ and $v_2$, is there a ...
4
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0answers
81 views

Indexing structure for all-pairs min-cuts in a huge DAG

I have a huge DAG - e.g., the dependency graph of all packages in a linux distribution. Suppose I'd like to make a user-friendly tool that makes it very easy to understand how to break the transitive ...
7
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1answer
269 views
9
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1answer
281 views

Finding similar vectors in subquadratic time

Let $d:\{0,1\}^k\times \{0,1\}^k \to \mathbb{R}$ be a function which we refer to as the similarity function. Examples of similarity function are cosine distance, $l_2$ norm, Hamming distance, Jaccard ...