We show that, for any fixed δ > 0, the combinatorial complexity of the union of n triangles in the plane, each of whose angles is at least δ, is O(n2^α(n) log* n), with the constant of proportionality depending on δ. This considerably improves the twenty-...

We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the ...

We provide improved bounds on the size of cache-oblivious range reporting data structures that achieve the optimal query bound of O(log_B N + K/B) block transfers. Our first main result is an O(N√log N log log N)-space data structure that achieves this ...

We investigate the deterministic and the randomized decision tree complexities of Boolean functions, denoted by D(f) and R(f), respectively. A long standing conjecture is that, for every Boolean function f, R(f) = Ω(D(f)α where α = log₂ (1+√33/4) = ...

Holant problems are a general framework to study counting problems. Both counting Constraint Satisfaction Problems (#CSP) and graph homomorphisms are special cases. We prove a complexity dichotomy theorem for Holant*(F), where F is a set of constraint ...

The Dichotomy Conjecture for Constraint Satisfaction Problems has been verified for conservative problems (or, equivalently, for list homomorphism problems) by Andrei Bulatov. An earlier case of this dichotomy, for list homomorphisms to undirected ...

We study the problem of testing isomorphism (equivalence up to relabelling of the variables) of two Boolean functions f,g: {0, 1}ⁿ → {0, 1}. Our main focus is on the most studied case, where one of the functions is given (explicitly) and the other ...

We consider the problem of approximating a signal P with another signal F consisting of a few piecewise constant segments. This problem arises naturally in applications including databases (e.g., histogram construction), speech recognition, ...

In the stochastic knapsack problem, we are given a set of items each associated with a probability distribution on sizes and a profit, and a knapsack of unit capacity. The size of an item is revealed as soon as it is inserted into the knapsack, and the ...

We consider various stochastic models that incorporate the notion of risk-averseness into the standard 2-stage recourse model, and develop novel techniques for solving the algorithmic problems arising in these models. A key notable feature of our work ...

We prove almost tight hardness results under randomized reductions for finding independent sets in bounded degree graphs and hypergraphs that admit a good coloring. Our specific results include the following (where Δ, a constant, is a bound on the ...

In the Discrepancy problem, we are given M sets {S₁,..., S_M} on N elements. Our goal is to find an assignment χ of {−1, + 1} values to elements, so as to minimize the maximum discrepancy max_j | Σ_iεSj χ(i)|. Recently, Bansal gave an efficient algorithm ...

Hardness results for maximum agreement problems have close connections to hardness results for proper learning in computational learning theory. In this paper we prove two hardness results for the problem of finding a low degree polynomial threshold ...

We study the approximability of two natural Boolean constraint satisfaction problems: Horn satisfiability and exact hitting set. Under the Unique Games conjecture, we prove the following optimal inapproximability and approximability results for finding ...

In a beautiful result, Raghavendra established optimal Unique Games Conjecture (UGC)-based inapproximability for a large class of constraint satisfaction problems (CSPs). In the class of CSPs he considers, of which Maximum Cut is a prominent example, ...

In modern wireless networks devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the ...

The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a sender-receiver pair located in a metric space, ...

Bargaining networks model the behavior of a set of players who need to reach pairwise agreements for making profits. Nash bargaining solutions in this context correspond to solutions which are stable and balanced. Kleinberg and Tardos [19] proved that, ...

We show that computing a relative---that is, multiplicative as opposed to additive---approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability ...

We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m > n selfish agents that unilaterally decide to move from one vetex to ...