Lower Bounds for Graph Exploration Using Local Policies

Mar 18, 2016 - e.g. a social network or the graph derived from the exploration of a geometric space. .... Graph with n vertices with a chain of n/7 ga...

0 downloads 5 Views 500KB Size

Recommend Documents

Mar 18, 2016 - 3 Rice University, Houston, TX, USA. sl28,[email protected] ... geometric exploration of a space by a robot, both of which have ... jacent edge with lowest value, i.e., oldest time stamp or least ... in a pre-established fashion.

Jan 31, 2012 - graph problems that would separate ID, OI, and PO from the perspective of local algorithms. Indeed, there are results that show that many problems that can be solved with a local algorithm in ID also admit a local algorithm in OI or PO

Dec 29, 2017 - (and spectral) approximation which may be of independent interest: any two d−regular graphs which approximate each other's cuts ... asymptotic savings by considering sketches which are not graphs. We also give a lowerbound for ... âˆ

Feb 8, 2016 - The main computational resource studied for this kind of algorithm is the amount of space it ... pass streaming algorithm requires an infeasible amount of main memory, it is natural to ask whether there exists a .... We start with a qui

Feb 19, 2015 - Hell and Nešetril showed that for any fixed simple graph H, the problem whether there exists a homomorphism from G .... every two vertices with a common neighbor in G are mapped onto distinct vertices in H. As ... neighbors of a verte

Oct 28, 2016 - combinatorial problems, which we call String Crafting and Orthog- ... 2Ω(|s|/ log |s|)-time lower bounds for (Induced) Subgraph and (Induced) Minor ..... part of the lemma. For the case that G is connected, we add to the graph G const

Jun 8, 2011 - LOWER BOUNDS FOR POLYNOMIALS USING GEOMETRIC PROGRAMMING. 3. We denote f0 and f2dǫi by f0 and f2d,i for short. Thus f has the form. (1) f = f0 + ∑ α∈Ω(f). fαXα + ...... [9] D. Knuth, The Art of Computer Programming, Volume 2, A

Feb 16, 2016 - Hell and Nešetril showed that for every fixed simple graph H, the problem whether there exists ... morphism f : G → H is called locally injective if for every vertex u ∈ V (G), its neighborhood is mapped injectively into the neigh

May 9, 2018 - Less is known regarding the complexity of general undirected graph ..... with a∗ bits of memory will visit less than 2Ω(a∗) distinct vertices.

Mar 31, 2016 - the network graph; they only know their own identifier and potential additional inputs. All nodes wake up simultaneously and computation proceeds in ... Γv := Γ1(v), that is, Γv is the (inclusive) neighborhood of v. ...... are r-equ

May 25, 2018 - such as “is there a better method for this problem than what we have?” and “what is the best ..... Our unified construction is thus also simpler in a ...

Sep 24, 2015 - CC] 24 Sep 2015 ...... Similarly add an arc from the in1 terminal of bi ... For i ≤ r we add arcs from xi to the in0 terminal of the gadgets a j. 1,j ∈ [.

Jun 20, 2008 - Y . Observe that so long as X and Y are consistent, fX(v) = fY (v) ⇐⇒ setX(v) = setY (v) for all vertices v, where setX is the function on G defined as setX(v)=1if v ∈ X and 0 otherwise. Fix a distribution Dx0,L for snakes of len

So to lower-bound the deterministic query complex- ity, it suffices to lower-bound the size of any cut that splits the graph into two reasonably large components.1.

Mar 6, 2006 - Many important combinatorial optimization problems arising in both theory and practice are NP- hard, which forces people to .... Ω(n6/5) if d = 4,. Ω(n3/4) if d = 3,. Ω(n2/5) if d = 2. (5). It is worth to note that to apply Theorem 1

May 14, 2008 - proximated or sign-represented by polynomials of low degree, linear-programming duality implies the existence of a certain dual object to witness that fact. This dual object, which is a real function or a probability distribution, reve

Feb 23, 2013 - rational approximation of α at level ε > 0, if. ||α − a|| < ε holds. (Here ||·|| denotes the norm associated with the usual hermitian product in Cn). A regular sequence f1,...,fn ∈ ZZ[X1,...,Xn] is said to be smooth if for any

of multidimensional datasets arising from a wide variety of applications ..... ( IP ). 1/N. R. Given that the factor matrices are load balanced up to a factor of δ, we see ...

Jun 3, 2011 - erature [CW09, KNW10] to prove lower bounds for linear algebra and norm estimation problems. Since the problem has communication complex- ity of Ω(d), the conclusion follows. We apply the argument to arbitrary matri- ces A by represent

Apr 2, 2011 - pure, we call a codimension-one face of K a ridge. The link of a face F ∈ K is lkK(F) = {G ∈ K : G ⊇ F}. .... Theorem 2.2 (Stanley [13], Billera-Lee [4]) A vector h = (h0,...,hd) ∈ Zd+1 is the h-vector of a simplicial d-polytope

(4.2). Bn(Q) = {f ∈ Rn : n−1. ∑ j=0 a2 j f2 j ≤ Q}. For a function f in the Sobolev-type ball Hβ(Q) its vector of coefficients belongs to Bn(Q) with a2 j =1 + λ. 2β/r.

Feb 1, 2008 - best lower bound is a lower bounds of 2.5n2 − o(n2), on the number of products needed to compute ... GF(2) has at least 3n2 − o(n2) product gates, and that any bilinear circuit for matrix product over the field ..... observations mo

Sep 26, 2013 - There has been significant recent progress in understanding the power of constant depth ... notes “with fanout.”) Similarly one may define quantum analogs of ACC(q) (called QACC(q)) and ACC (called QACC). Thus the equivalence of fa

|φj(E)|sj . Lemma 4.2: The solution of the linear program min 1T s subject to ∆ · s ≥ 1 and s ≥ 0, .... contains exactly M loads and stores, except the last segment ...... [Online]. Available: http://arxiv.org/abs/1702.02017. [9] G. Ballard,