arXiv subjects

Jittat Fakcharoenphol

Publications and source records attributed to Jittat Fakcharoenphol.

16 recordsLinked to original sources

arXiv2026

Subdomain-aware representation compression for pretrained image embeddings

Dimensionality reduction is a well-known technique for improving space efficiency, typically applied uniformly across an entire dataset. This paper investigates the possibilities of using dimensionality reduction techniques for subdomain representation compression. We explore standard techniques such as Principal Component Analysis (PCA) and Linear discriminant analysis (LDA) in image domains. The results not only demonstrate the expected improvements in space and computation complexity crucial for edge-device ML applications but also show improvements in accuracy over direct full-embedding procedure. One possible explanation is that dimensionality reduction effectively extracts subdomain features. We also performed experiments to demonstrate transfer learning capabilities using the compressed representations.

cs.LG↗

arXiv2026

An Improved Linear Extractable Sketch Data Structure for Flow Count Statistics

Sketch data structures are very useful for computing statistics on streaming data, including network traffic, server requests, and financial transactions. In recent work, FermatSketch was introduced as an underlying data structure used to monitor changes in network states. It is a linear data structure that maintains an associated array of counters and supports listing all key-counter pairs while using almost linear space. Because it is linear, it can be used to monitor changes between two streams with space proportional to the number of items that change. The data structure is based on a hash table, and all key-counter pairs can be successfully listed when there are slots in the table with exactly one key hashed to them. We show how to relax this requirement by using additional computational resources when listing the key-counter pairs, thereby improving space efficiency with only a small overhead when collecting statistics. We achieve this by storing, for each bucket, multiple linear combinations of the counters whose coefficients are generated from the keys. With this information, certain linear systems can be solved to obtain the key-counter pairs. A preliminary experiment shows a significant reduction of memory needed for the data structure. Our work can be viewed as a trade-off between space and time.

cs.DS↗

arXiv2026

Covering Planar Lattices with Interior-Disjoint Unit Disks

We study an infinite variant of the coin-covering problem for periodic point sets in the plane. Given a point set of spacing $d$, we ask whether all of its points can be covered by pairwise non-overlapping unit disks. We consider the triangular lattice, the square lattice, and the honeycomb point set, and construct periodic motif patterns that certify several intervals of coverable spacings. For the triangular lattice, our constructions include single-family patterns with vertex, face, and off-lattice realizing centers, as well as multi-family patterns. For the honeycomb point set, additional native motifs fill gaps left by the triangular-lattice constructions. For the square lattice, we revisit the constructions of Alm et al., identify an unintended overlap in one motif realization, and give new patterns that recover part of the affected interval and establish an additional coverability interval.

cs.CG↗

arXiv2026

Robust Bichromatic Classification in 3D Using Planes and Slices

Given two sets of points in 3-dimensional space $R$ and $B$, we want to separate these two sets of points using a classifier based on linear constraints, while ensuring robustness against outliers. The problem was studied in $\mathbb{R}^2$ by Glazenburg et al. We follow their approach and present various algorithms for many types of classifiers under various definitions of outliers. Our algorithms rely mainly on the duality of points and planes in $\mathbb{R}^3$.

cs.CG↗

arXiv2023

An Improved PTAS for Covering Targets with Mobile Sensors

This paper considers a movement minimization problem for mobile sensors. Given a set of $n$ point targets, the $k$-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at $k$ base stations, to cover all targets minimizing the total moving distance of the sensors. We present a polynomial-time approximation scheme for finding a $(1+ε)$ approximate solution running in time $n^{O(1/ε)}$ for this problem when $k$, the number of base stations, is constant. Our algorithm improves the running time exponentially from the previous work that runs in time $n^{O(1/ε^2)}$, without any target distribution assumption. To devise a faster algorithm, we prove a stronger bound on the number of sensors in any unit area in the optimal solution and employ a more refined dynamic programming algorithm whose complexity depends only on the width of the problem.

cs.CG↗

arXiv2023

Folding Every Point on a Polygon Boundary to a Point

We consider a problem in computational origami. Given a piece of paper as a convex polygon $P$ and a point $f$ located within, fold every point on a boundary of $P$ to $f$ and compute a region that is safe from folding, i.e., the region with no creases. This problem is an extended version of a problem by Akitaya, Ballinger, Demaine, Hull, and Schmidt~[CCCG'21] that only folds corners of the polygon. To find the region, we prove structural properties of intersections of parabola-bounded regions and use them to devise a linear-time algorithm. We also prove a structural result regarding the complexity of the safe region as a variable of the location of point $f$, i.e., the number of arcs of the safe region can be determined using the straight skeleton of the polygon $P$.

cs.CG↗

arXiv2023

Stochastic Contextual Bandits with Graph-based Contexts

We naturally generalize the on-line graph prediction problem to a version of stochastic contextual bandit problems where contexts are vertices in a graph and the structure of the graph provides information on the similarity of contexts. More specifically, we are given a graph $G=(V,E)$, whose vertex set $V$ represents contexts with {\em unknown} vertex label $y$. In our stochastic contextual bandit setting, vertices with the same label share the same reward distribution. The standard notion of instance difficulties in graph label prediction is the cutsize $f$ defined to be the number of edges whose end points having different labels. For line graphs and trees we present an algorithm with regret bound of $\tilde{O}(T^{2/3}K^{1/3}f^{1/3})$ where $K$ is the number of arms. Our algorithm relies on the optimal stochastic bandit algorithm by Zimmert and Seldin~[AISTAT'19, JMLR'21]. When the best arm outperforms the other arms, the regret improves to $\tilde{O}(\sqrt{KT\cdot f})$. The regret bound in the later case is comparable to other optimal contextual bandit results in more general cases, but our algorithm is easy to analyze, runs very efficiently, and does not require an i.i.d. assumption on the input context sequence. The algorithm also works with general graphs using a standard random spanning tree reduction.

cs.LG↗

arXiv2021

Retraction: Improved Approximation Schemes for Dominating Set Problems in Unit Disk Graphs

Retraction note: After posting the manuscript on arXiv, we were informed by Erik Jan van Leeuwen that both results were known and they appeared in his thesis[vL09]. A PTAS for MDS is at Theorem 6.3.21 on page 79 and A PTAS for MCDS is at Theorem 6.3.31 on page 82. The techniques used are very similar. He noted that the idea for dealing with the connected version using a constant number of extra layers in the shifting technique not only appeared Zhang et al.[ZGWD09] but also in his 2005 paper [vL05]. Finally, van Leeuwen also informed us that the open problem that we posted has been resolved by Marx~[Mar06, Mar07] who showed that an efficient PTAS for MDS does not exist [Mar06] and under ETH, the running time of $n^{O(1/ε)}$ is best possible [Mar07]. We thank Erik Jan van Leeuwen for the information and we regret that we made this mistake. Abstract before retraction: We present two (exponentially) faster PTAS's for dominating set problems in unit disk graphs. Given a geometric representation of a unit disk graph, our PTAS's that find $(1+ε)$-approximate solutions to the Minimum Dominating Set (MDS) and the Minimum Connected Dominating Set (MCDS) of the input graph run in time $n^{O(1/ε)}$. This can be compared to the best known $n^{O(1/ε \log {1/ε})}$-time PTAS by Nieberg and Hurink~[WAOA'05] for MDS that only uses graph structures and an $n^{O(1/ε^2)}$-time PTAS for MCDS by Zhang, Gao, Wu, and Du~[J Glob Optim'09]. Our key ingredients are improved dynamic programming algorithms that depend exponentially on more essential 1-dimensional "widths" of the problems.

cs.DS↗

arXiv2021

Bandit Multiclass Linear Classification for the Group Linear Separable Case

We consider the online multiclass linear classification under the bandit feedback setting. Beygelzimer, Pál, Szörényi, Thiruvenkatachari, Wei, and Zhang [ICML'19] considered two notions of linear separability, weak and strong linear separability. When examples are strongly linearly separable with margin $γ$, they presented an algorithm based on Multiclass Perceptron with mistake bound $O(K/γ^2)$, where $K$ is the number of classes. They employed rational kernel to deal with examples under the weakly linearly separable condition, and obtained the mistake bound of $\min(K\cdot 2^{\tilde{O}(K\log^2(1/γ))},K\cdot 2^{\tilde{O}(\sqrt{1/γ}\log K)})$. In this paper, we refine the notion of weak linear separability to support the notion of class grouping, called group weak linear separable condition. This situation may arise from the fact that class structures contain inherent grouping. We show that under this condition, we can also use the rational kernel and obtain the mistake bound of $K\cdot 2^{\tilde{O}(\sqrt{1/γ}\log L)})$, where $L\leq K$ represents the number of groups.

cs.LG↗

arXiv2021

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$

For any $ε>0$, Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a $(1+ε)$-approximate solution to the $k$-hop MST problem in the Euclidean plane that runs in time $(n/ε)^{O(k/ε)}$. In this paper, we present an algorithm that runs in time $(n/ε)^{O(\log k \cdot(1/ε)^2\cdot\log^2(1/ε))}$. This gives an improvement on the dependency on $k$ on the exponent, while having a worse dependency on $ε$. As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.

cs.DS↗

arXiv2021

Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities

We consider a fairness problem in resource allocation where multiple groups demand resources from a common source with the total fixed amount. The general model was introduced by Elzayn et al. [FAT*'19]. We follow Donahue and Kleinberg [FAT*'20] who considered the case when the demand distribution is known. We show that for many common demand distributions that satisfy sharp lower tail inequalities, a natural allocation that provides resources proportional to each group's average demand performs very well. More specifically, this natural allocation is approximately fair and efficient (i.e., it provides near maximum utilization). We also show that, when small amount of unfairness is allowed, the Price of Fairness (PoF), in this case, is close to 1.

cs.LG↗

arXiv2018

Finding All Useless Arcs in Directed Planar Graphs

We present a linear-time algorithm for simplifying flow networks on directed planar graphs: Given a directed planar graph on $n$ vertices, a source vertex $s$ and a sink vertex $t$, our algorithm removes all the arcs that do not participate in any simple $s,t$-path in linear-time. The output graph produced by our algorithm satisfies the prerequisite needed by the $O(n\log n)$-time algorithm of Weihe [FOCS'94 \& JCSS'97] for computing maximum $s,t$-flow in directed planar graphs. Previously, Weihe's algorithm could not run in $O(n\log n)$-time due to the absence of the preprocessing step; all the preceding algorithms run in $\tildeΩ(n^2)$-time [Misiolek-Chen, COCOON'05 \& IPL'06; Biedl, Brejov{á} and Vinar, MFCS'00]. Consequently, this provides an alternative $O(n\log n)$-time algorithm for computing maximum $s,t$-flow in directed planar graphs in addition to the known $O(n\log n)$-time algorithms [Borradaile-Klein, SODA'06 \& J.ACM'09; Erickson, SODA'10]. Our algorithm can be seen as a (truly) linear-time $s,t$-flow sparsifier for directed planar graphs, which runs faster than any maximum $s,t$-flow algorithm (which can also be seen of as a sparsifier). The simplified structures of the resulting graph might be useful in future developments of maximum $s,t$-flow algorithms in both directed and undirected planar graphs.

cs.DS↗

arXiv2017

Learning Network Structures from Contagion

In 2014, Amin, Heidari, and Kearns proved that tree networks can be learned by observing only the infected set of vertices of the contagion process under the independent cascade model, in both the active and passive query models. They also showed empirically that simple extensions of their algorithms work on sparse networks. In this work, we focus on the active model. We prove that a simple modification of Amin et al.'s algorithm works on more general classes of networks, namely (i) networks with large girth and low path growth rate, and (ii) networks with bounded degree. This also provides partial theoretical explanation for Amin et al.'s experiments on sparse networks.

cs.LG↗

arXiv2013

A simpler load-balancing algorithm for range-partitioned data in peer-to-peer systems

Random hashing is a standard method to balance loads among nodes in Peer-to-Peer networks. However, hashing destroys locality properties of object keys, the critical properties to many applications, more specifically, those that require range searching. To preserve a key order while keeping loads balanced, Ganesan, Bawa and Garcia-Molina proposed a load-balancing algorithm that supports both object insertion and deletion that guarantees a ratio of 4.237 between the maximum and minimum loads among nodes in the network using constant amortized costs. However, their algorithm is not straightforward to implement in real networks because it is recursive. Their algorithm mostly uses local operations with global max-min load information. In this work, we present a simple non-recursive algorithm using essentially the same primitive operations as in Ganesan {\em et al.}'s work. We prove that for insertion and deletion, our algorithm guarantees a constant max-min load ratio of 7.464 with constant amortized costs.

cs.DC↗

arXiv2012

Faster Algorithms for Semi-Matching Problems

We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the weighted case, we give an $O(nm\log n)$-time algorithm, where $n$ is the number of vertices and $m$ is the number of edges, by exploiting the geometric structure of the problem. This improves the classical $O(n^3)$ algorithms by Horn [Operations Research 1973] and Bruno, Coffman and Sethi [Communications of the ACM 1974]. For the unweighted case, the bound could be improved even further. We give a simple divide-and-conquer algorithm which runs in $O(\sqrt{n}m\log n)$ time, improving two previous $O(nm)$-time algorithms by Abraham [MSc thesis, University of Glasgow 2003] and Harvey, Ladner, Lovász and Tamir [WADS 2003 and Journal of Algorithms 2006]. We also extend this algorithm to solve the \textit{Balance Edge Cover} problem in $O(\sqrt{n}m\log n)$ time, improving the previous $O(nm)$-time algorithm by Harada, Ono, Sadakane and Yamashita [ISAAC 2008].

cs.DS↗

arXiv2008

Low congestion online routing and an improved mistake bound for online prediction of graph labeling

In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of $α$ on any edge, there exists an online prediction algorithm with mistake bound $α$ times the cut size, which is the size of the cut induced by the label partitioning of graph vertices. With previous known bound of $O(\log n)$ for $α$ for the routing problem on trees with $n$ vertices, we obtain an improved prediction algorithm for graphs with high effective resistance. In contrast to previous approaches that move the graph problem into problems in vector space using graph Laplacian and rely on the analysis of the perceptron algorithm, our proof are purely combinatorial. Further more, our approach directly generalizes to the case where labels are not binary.

cs.DS↗