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In this paper, we address the problem of joint Resource Block (RB) allocation and Modulation-and-Coding Scheme (MCS) selection for LTE femtocell DownLink (DL). We first formulate the problem as an Integer Linear Program (ILP) whose objective is to minimize the number of allocated RBs of a closed femtocell, while guaranteeing minimum throughput for each user. In view of the NP-hardness of the ILP,...
We give a new and improved proof that the shrinkage exponent of De Morgan formulae is 2. Namely, we show that for any Boolean function f : {0,1}n → {0,1}, setting each variable out of x1,,xn with probability 1 -- p to a randomly chosen constant, reduces the expected formula size of the function by a factor of O(p2). This result is tight and improves the work of Håstad [SIAM...
We prove exponential lower bounds on the size of homogeneous depth 4 arithmetic circuits computing an explicit polynomial in VP. Our results hold for the Iterated Matrix Multiplication polynomial - in particular we show that any homogeneous depth 4 circuit computing the (1,1) entry in the product of n generic matrices of dimension nO(1) must have size nΩ(√n). Our results...
There has been a recent surge of interest in the role of information in strategic interactions. Much of this work seeks to understand how the realized equilibrium of a game is influenced by uncertainty in the environment and the information available to players in the game. Lurking beneath this literature is a fundamental, yet largely unexplored, algorithmic question: how should a "market maker"...
For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertex-cover number (equivalently, the size of the maximum matching in C is bounded), then #Sub(C) is polynomial-time solvable. We complement this result with a corresponding lower bound: if C is any...
We show that it is quasi-NP-hard to color 2-colorable 12-uniform hypergraphs with 2(log n) O(1) colors where n is the number of vertices. Previously, Guruswami et al. [1] showed that it is quasi-NP-hard to color 2-colorable 8-uniform hypergraphs with 22 O(vlog log n) colors. Their result is obtained by composing a standard Outer PCP with an Inner PCP based on the Short Code of super-constant degree...
We show that an effective version of Siegel's Theorem on finiteness of integer solutions for a specific algebraic curve and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the k >= 3 domain elements...
We show here a 2Ω(√d ⋅ log N) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d3 in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Σi ∏j Qij, where the Qij's...
We consider the problem of verifying the identity of a distribution: Given the description of a distribution over a discrete support p = (p1, p2,, pn) how many samples (independent draws) must one obtain from an unknown distribution, q, to distinguish, with high probability, the case that p = q from the case that the total variation distance (L1 distance) ||p -- q|| 1≥ ε?...
The analysis of network routing games typically assumes, right at the onset, precise and detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desirable target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve...
We give a fixed-parameter tractable algorithm that, given a parameter k and two graphs G1, G2, either concludes that one of these graphs has treewidth at least k, or determines whether G1 and G2 are isomorphic. The running time of the algorithm on an n-vertex graph is 2O(k5 log k) n5, and this is the first fixed-parameter algorithm for Graph Isomorphism parameterized by treewidth. Our algorithm in...
We introduce a new and natural algebraic proof system, which has tight connections to (algebraic) circuit complexity. In particular, we show that any super-polynomial lower bound on any Boolean tautology in our proof system implies that the permanent does not have polynomial-size algebraic circuits (VNP ≠ VP). As a corollary, super-polynomial lower bounds on the number of lines in Polynomial...
We prove the following hardness result for anatural promise variant of the classical CNF-satisfiabilityproblem: Given a CNF-formula where each clause has widthw and the guarantee that there exists an assignment satisfyingat least g = [w/2] -- 1 literals in each clause, it is NP-hard tofind a satisfying assignment to the formula (that sets at leastone literal to true in each clause). On the other hand,...
This paper presents a new model to verify behavioral equivalences based on behavior ontology. In the ontology, actions among processes or tasks are defined as interaction and movement, and, further, behaviors are defined as a sequence of such interactions and/or movements. Since some interactions and movements among the behaviors are overlapped, the behaviors are organized in a lattice structure,...
The propositional interval logic of temporal neighborhood (PNL for short) features two modalities that make it possible to access intervals adjacent to the right (modality xAy) and to the left (modality xAy) of the current interval. PNL stands at a central position in the realm of interval temporal logics, as it is expressive enough to encode meaningful temporal conditions and decidable (undecidability...
We study optimal equilibrium in turn based multiplayer mean-payoff games. Nash equilibrium are a standard way to define rational behaviour of different players in multi-player games. These equilibrium treat all players equally. We study settings where a leader has additional power over the game: she has the power to assign strategies to all participating players, including herself. We argue that a...
Temporal functional dependencies (TFDs) add valid time to classical functional dependencies (FDs) in order to express data integrity constraints over the flow of time. If the temporal dimension adopted is an interval, we have to deal with interval-based temporal functional dependencies (ITFDs for short), which consider different interval relations between valid times of related tuples. The related...
In this paper, Subset Sum problem (Non Polynomial Complete problem) and analysis of its two solutions is discussed. These solutions are the Dynamic Solution algorithm and the Randomized algorithm. Dynamic Solution is a sound and complete algorithm that can be used to determine satisfiability and unsatisfiability with certainty. Randomized Algorithm can determine satisfiablity as well as the solution...
We introduce a probabilistically complete algorithm for solving a visibility-based pursuit-evasion problem in two-dimensional polygonal environments with multiple pursuers. The inputs for our algorithm are an environment and the initial positions of the pursuers. The output is a joint strategy for the pursuers that guarantees that the evader has been captured. We create a Sample-Generated Pursuit-Evasion...
Guess and determine (GD) attack is one of the general attacks on stream ciphers. Heuristic guess and determine (HGD) attack is a class of GD attacks designed algorithmically for classes of stream ciphers, holding a certain condition that the variables are of the same size. In this Paper, we introduce an improved version of HGD attack, called IHGD. Using this method, the authors examine the resistant...
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