Metric facility location and K-means are well-known problems of combinatorial optimization. Both admit a fairly simple heuristic called single-swap, which adds, drops or swaps open facilities until it reaches a local optimum. For both problems, it is known that this algorithm produces a solution that is at most a constant factor worse than the respective global optimum. In this paper, we show t...

We develop a new bisimulation (pseudo)metric for weighted finite automata (WFA) that generalizes Boreale’s linear bisimulation relation. Our metrics are induced by seminorms on the state space of WFA. Our development is based on spectral properties of sets of linear operators. In particular, the joint spectral radius of the transition matrices of WFA plays a central role. We also study continui...

Given a metric graph G, we are concerned with finding a spanning tree of G where the maximum weighted degree of its vertices is minimum. In a metric graph (or its spanning tree), the weighted degree of a vertex is defined as the sum of the weights of its incident edges. In this paper, we propose a 4.5-approximation algorithm for this problem. We also prove it is NP-hard to approximate this prob...

The first general decomposition theorem for the k-server problem is presented. Whereas all previous theorems are for the case of a finite metric with k + 1 points, the theorem given here allows an arbitrary number of points in the underlying metric space. This theorem implies O(polylog(k))-competitive algorithms for certain metric spaces consisting of a polylogarithmic number of widely separate...

In this paper, we propose an automatic method for the objective evaluation of segmentation results. The method is based on computing the deviation of the segmentation results from a reference segmentation. The discrepancy between two results is weighted based on spatial and temporal contextual information, by taking into account the way humans perceive visual information. The metric is useful f...

The performance of keyword search systems depends heavily on the quality of confidence scores. In this work, a novel discriminative score calibration method has been proposed. By training an MLP classifier employing the word posterior probability and several novel normalized scores, we can obtain a relative improvement of 4.67% for the actual term-weighted value (ATWV) metric on the OpenKWS15 d...

We consider the worst-case weighted sum-rate maximization (WSRMax) problem under imperfect channel state information in multicell downlink multi-input single-output systems. The problem is known to be NP-hard. We propose a solution method, based on semi-definite relaxation and branch and bound technique, which solves globally the noncovex robust WSRMax problem with an optimality certificate. Th...

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric...