By Fan Chung, Alexander Tsiatas (auth.), Anthony Bonato, Jeannette Janssen (eds.)

This e-book constitutes the refereed complaints of the ninth overseas Workshop on Algorithms and versions for the Web-Graph, WAW 2012, held in Halifax, Nova Scotia, Canada, in June 2012. The thirteen papers awarded have been conscientiously reviewed and chosen for inclusion during this quantity. They deal with a couple of subject matters concerning the advanced networks such hypergraph coloring video games and voter versions; algorithms for detecting nodes with huge levels; random Appolonian networks; and a sublinear set of rules for Pagerank computations.

**Read Online or Download Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings PDF**

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**Extra info for Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings**

**Example text**

We may assume that this property holds for all i. Therefore, the maximum radius of inﬂuence of vi is O((log 2 t/i)1/m ). We will investigate how many edges are in the cut by counting (independently) edges in this cut directed to vertices of similar age. For a given integer k such that 0 ≤ k < log t, let V (k) = {vi ∈ Vt : ek ≤ i < min{ek+1 , t}}, E (k) = {(vi , vj ) ∈ Et : vi ∈ V (k) and i < j ≤ t} C (k) = E (k) ∩ E(Vt , Vt ). It is clear that {E (k) : 0 ≤ k < log t} is a partition of the edge set and so {C (k) : 0 ≤ k < log t} is a partition of the cut E(Vt , Vt ).

Mehrabian Algorithm 1 . Calculate OPT(t, P, F , D) 1: if t has no child then 2: OPT(t, P, F, D) = 0 3: else 4: t ← the child of t · for some vertex v then 5: if V (Wt ) is V (Wt )∪{v} 6: OPT(t, P, F, D) = min{OPT(t , Q, F, D) : Q ∈ P ∗ v} 7: else if V (Wt ) is V (Wt ) \ {v} for some vertex v ∈ V (Wt ) then 8: P ← the element of P containing v 9: if P = {v} then 10: OPT(t, P, F, D) = OPT(t , P \ {{v}}, F \ {v}, D/v) 11: else if v ∈ F then 12: if there is a u ∈ P \ {v} with u ∈ F then 13: OPT(t, P, F, D) = OPT(t , P/v, F \ {v}, D/v) 14: else 15: OPT(t, P, F, D) = ∞ 16: end if 17: else if there is a u ∈ P \ {v} with (v, u) ∈ D then 18: OPT(t, P, F, D) = OPT(t , P/v, F \ {v}, D/v) 19: else 20: if for all u ∈ P \ {v} we have u ∈ /F and for some u ∈ P \ {v} we have (u, v) ∈ D then 21: OPT(t, P, F, D) = OPT(t , P/v, F ∪ {u ∈ P \ {v} : (u, v) ∈ D}, D/v) 22: else 23: OPT(t, P, F, D) = ∞ 24: end if 25: end if 26: else if Wt is Wt ∪ {(u, v)} for some arc (u, v) then 27: t ← the child of t 28: if u and v are in diﬀerent elements of P then 29: OPT(t, P, F, D) = w(u, v) + OPT(t , P, F, D) 30: else 31: S ← {x ∈ V (Wt ) : (x, u) ∈ D} ∪ {u} 32: T ← {y ∈ V (Wt ) : (v, y) ∈ D} ∪ {v} 33: D ← D ∪ {(x, y) : x ∈ S, y ∈ T } 34: if v ∈ F then 35: F ←F ∪S 36: else 37: F ←F 38: end if 39: OPT(t, P, F, D) = min {w(u, v) + OPT(t , P, F, D), OPT(t , P, F , D )} 40: end if 41: end if 42: end if On a DAG Partitioning Problem 25 F ⊆ X and D ⊆ X × X , then (t, P, F , D) is the DAG Partitioning problem conﬁned to H with the following extra restrictions: – Vertices in F should not have their sink in H; – Vertices in the same element of P should have the same sink, and vertices in diﬀerent elements should have distinct sinks; and the following assumptions about G − H: – Vertex v ∈ X is in F if and only if v has a path in G − H to its sink, and the sink of v is out of H.

Then, PageRank(u) = n. u∈V PageRank has been used by the Google search engine and has found applications in wide range of data analysis problems [4, 7]. In this context, the problem of identifying “signiﬁcant” vertices could be illustrated by the following search problem: Let Top PageRanks denote the problem of identifying all vertices whose PageRanks in a network G = (V, E) are more than a given threshold value 1 ≤ Δ ≤ |V |. In this paper, we consider for the following close variant of Top PageRanks: Significant PageRanks: Given a network G = (V, E), a threshold value 1 ≤ Δ ≤ |V | and a positive constant c > 1, compute, with success probability 1 − o(1), a subset S ⊆ V with the property that S contains all vertices of PageRank at least Δ and no vertex with PageRank less than Δ/c.